Off contract at United in June, Maguire has offers from Al-Ettifaq and Cristiano Ronaldo's Al-Nassr worth £500,000-a-week - net.
Asked what Maguire should do, former England centre-half Pallister told Tribalfootball.com: "That's a personal choice.
"It depends how he sees it. It's very hard at this stage of your career to turn that kind of money down, I would suggest.
"He's finding himself out of the team at the moment. His contract's running down. I don't know whether there'll be any conversations about a new contract. I would have thought they would have started that."
Pallister continued: "But listen, Harry Maguire's never let Manchester United down. I know he's had that dip in form and he had a lot of people on his back, especially the media. He got through that crisis. He was a consummate professional. I think he was one of our better players last season, in amongst what was a torrid season.
"You know what you're gonna get from Harry. I think if he was to leave, he would leave with everybody's blessing. As I say, very hard to turn down that kind of money at a latter stage of your career when you start thinking about retirement and what you're going to have in your kitty to survive without football."
Why I decided to leave United
Pallister left United at 33, a similar age to Maguire, to return home to Middlesbrough. He admits he returned to Teesside in order to play regularly, though admits some regrets about the decision.
He said: "I think that's always in you (to play regularly). You wouldn't want to be sitting on the sidelines and watching. It's not what you do. I never, I never did that. You know, Sir Alex (Ferguson) sort said to me, 'You won't maybe play as many games as you would like the following season'. And he gave me the choice to leave or stay.
"But for the fact it was my hometown club came knocking and going back to Middlesbrough, I probably would have seen my year out and then left on a free. But I also didn't want to get frustrated being at United and not playing, because it was something I was used to for the nine years that I was there."
Regrets
Pallister continued: "So I had to weigh that all into the situation and make not just an emotional decision but a professional decision. And it was to leave. Do I have regrets? Kind of. I wish I'd have stayed the year. Obviously it was an exceptional year in '89.
"(Also) in terms of putting pressure on myself going back to Middlesbrough because they paid more for me to come back than they did when I left Middlesbrough. It was £2.3m (a British record for a defender at the time) they bought me for and they sold me for £2.5m, so... if I'd have left on a free, it might have been a bit different and the pressure wouldn't have been there if I'd have left it a year later, it would all have been different.
"But I put myself under pressure at Middlesbrough to be successful, which at times kind of hindered me a little bit."
- Gary Pallister was speaking to Tribalfootball on behalf of NewBettingOffers.co.uk