United signed Andre Onana from Inter Milan in a deal worth around £47million this summer but he has fallen below expectations so far.
The goalkeeper has conceded 33 goals in 20 appearances, including three in their 3-3 Champions League draw with Galatasaray on Wednesday.
Onana has been criticised for his efforts in the Turkish side's second goal in particular as he allowed Hakim Ziyech's free-kick to spill in.
As a result, Ramsdale has been suggested as a potential option for United amid his lack of game time at Arsenal.
Ramsdale has been usurped by David Raya in the Gunners goal, with talkSPORT's Brazil asking: "Onana is an accident waiting to happen - what about Ramsdale at Manchester United?"
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"I don't think so," his Breakfast co-host Gabby Agbonlahor replied. "I don't think Arsenal would sell him, I feel [Mikel] Arteta will want him as back-up."
"Why? I think if Ramsdale wants to go, he'll get a move. He's not playing!" said Brazil, before Gabby added: "With what Man United paid for Onana, I can't see them going out and buying another goalkeeper."
However, Brazil pointed towards the incoming investment from Sir Jim Ratcliffe as a potential catalyst for change in the United goal.
"But there's a new owner coming in now, he's putting in £1.3billion, he might say: 'Right, I'm now in charge of transfers - he goes. We're not going to win anything with him.'
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"Which would be harsh on Onana because he's a good shot stopper at times and he's made some good saves. But you don't become a multi-billionaire by luck, Sir Jim Ratcliffe will be ruthless.
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"He might just say: 'We've got to get rid of the deadwood now, I want us at the top again. This is not good enough just qualifying for the Champions League. We want to be the champions of England and favourites to win the Champions League.'
"That's the way he's got to think if he's putting that kind of money in."
England international Ramsdale has made only eight appearances for Arsenal this season amid the arrival of Raya on loan from Brentford.
He had been the Gunners' no.1 since signing from Sheffield United in 2021 but is no longer the first choice.
A move to Old Trafford would be a surprising one but if he's eyeing a starting role at Euro 2024, then it may be a wise move for game time.