The 26-year-old has reportedly been fined £650,000 for his antics, the equivalent of two weeks' wages.
Gascoigne, one of the most talented footballers England has ever produced, allowed his career to be derailed by drink as he struggled to cope with the limelight.
'I really like Marcus Rashford. He is my favourite England player. But you can tell things are just not right for him right now,' Gascoigne, 56, told the Daily Mirror.
Paul Gascoigne has urged trouble Manchester United star Marcus Rashford 'don't make the same mistakes I did' after he went on a boozy night out in Belfast last week
Former England star Gascoigne saw his own career derailed by alcohol in the 1990s
Gascoigne's infamous 'Dentist's Chair' celebration after scoring for England against Scotland at Euro '96 referenced a boozy pre-tournament night out in Hong Kong
'I would say to him, "Don't make the same mistakes as me". He may need the help of the players around him, the staff to bring him around. Sometimes there are problems outside the game.
'He is a great player, at a great club, playing for his country, and yet he doesn't seem happy.
'Obviously there is an issue with the manager [Erik ten Hag] and he doesn't even celebrate his goals in the same way. He is down, he is getting fined, like I was at Lazio. It is not easy being in the limelight.'
Former Newcastle and Tottenham star Gazza - best remembered for his brilliance for England at Euro '96 and cheeky 'Dentist's Chair' celebration in reference to a drunken night out in Hong Kong - recommended that Rashford gets counselling.
'Even footballers need it sometimes. Marcus is earning a fortune, at one of the biggest clubs in the world, everyone think you do not have a care in the world. But the pressure is not always easy,' he added.
Gascoigne urged Rashford to stop and think about the repercussions of going on a night out, saying the last time he went on a similar bender, he 'ended up in rehab'.
Rashford attended United's training session on Wednesday morning last week then flew by private jet to Belfast in the afternoon.
Rashford was reminded by a friend that he had training the next day but wanted to stay out
The footballer stayed at the five-star Fitzwilliam Hotel during his trip to Belfast last week
After arriving in Belfast on Wednesday Rashford went to the Dirty Onion pub (left) and Lavery's bar (right)
Rashford went to Thompsons Garage nightclub (pictured) after midnight, having spent the afternoon drinking with his entourage and waitress, Sarah Adair
He checked into the five-star Fitzwilliam Hotel before going out for drinks at the Dirty Onion pub and Lavery's Bar.
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On Thursday, Rashford visited his friend and former United team-mate Ro-Shaun Williams at his new club Larne FC, posing for pictures with coaching staff and academy players.
Reports then said Rashford and his entourage went to an Italian restaurant on Thursday afternoon.
Sarah Adair, a waitress at the restaurant, told The Sun that the footballer was 'clearly on a mission to get drunk' and was downing shots of tequila and cocktails.
Rashford didn't touch the sea bass he ordered and wouldn't eat the bruschetta because the tomatoes had seeds in them.
Despite being reminded by a friend he had training with United the following morning, Rashford was adamant he wanted to stay out.
The group were spotted at the nightclub Thompson's Garage, leaving somewhere between 1am and 2am.
Adair claimed she had to put Rashford to bed in the £1,500-a-night residence suite at his hotel.
Waitress Sarah Adair, pictured, said she was invited on a night out with the footballer and his entourage after they visited the Italian restaurant she worked in
Rashford had two nights out in Belfast last week and then called in sick for training on Friday
The night kicked off with a trip to Italian restaurant Villa Italia (pictured), where Rashford and his entourage enjoyed food and drinks
Timeline of Marcus Rashford's trip to Belfast and the fallout
Wednesday, January 24
9.55am Rashford arrives for training with Manchester United in the morning.
4.21pm In the afternoon he leaves Manchester on a private jet bound for Belfast.
5.17pm On arriving in the Northern Irish capital he checks in at the Fitzwilliam Hotel. The footballer and his entourage then go to the Dirty Onion pub and Lavery's bar.
Thursday, January 25
1.06pm The footballer is pictured visiting Larne FC, where his friend Ro-Shaun Williams has just signed.
2pm He goes to an Italian restaurant with his entourage and two women, where he meets Sarah Adair.
4.30pm The group leave the restaurant in the afternoon, before going to Villa Italia in the evening.
Friday, January 26
12.30am Rashford and his group go to Thompson's Garage nightclub.
2am The group leave and head back to the Fitzwilliam Hotel. Sources close to the player insist this was at 1.15am.
2.50am Rashford passes out fully clothed in his hotel room.
5am The footballer and his minders leave the hotel.
7am They board a private jet at Belfast airport.
8am Rashford touches down in Manchester and calls in sick for training.
Sunday, January 28
The striker is dropped for Manchester United's FA Cup match away at Newport County. Manager Erik Ten Hag vows to deal with the 'internal matter'.
Monday, January 29
8.45am Rashford arrives at training with his agent brother Dwaine Maynard, where he has talks with Ten Hag and football director John Murtough.
She said: 'He was so drunk at this point that he picked up his own bag and dropped it and all this cash fell out. It was all £20 notes and big wads of it. I reckon there was between £8,000 and £10,000 cash.
'Then he falls back into the wall and I have to kind of scoop him up and on to the bed. He was fully dressed and I reckon he just passed out like that.'
Rashford and his minders reportedly left the hotel around 5am to get his private jet back to Manchester. He did not report for training after calling in sick.
When pictures and videos of his Belfast night out emerged, Rashford was dropped from Ten Hag's squad for Sunday's FA Cup fourth round tie at Newport County.
The club released a statement on Monday evening confirming Rashford had 'taken responsibility' for his actions and they considered the matter closed.
Rashford scored within five minutes of his return to the United team at Wolves on Thursday
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