Willy Caballero is to leave the club at the end of his contract but City are widely tipped to sign Ederson from Benfica in the coming weeks to compete for the number one spot with Claudio Bravo.
Seaman suggested Hart's future could be impacted if David de Gea leaves United to join Real Madrid but would be delighted to see him at Emirates Stadium, although he accepts that the England international is unlikely to join a club where he will not be first choice.
"Top clubs will be after him but it's going to be a chain reaction because there's all the speculation about David de Gea, whether he goes to Real Madrid or not," Seaman, who spent one season at City after leaving Arsenal in 2003, told Omnisport.
"If that happens there'll be movement and at the moment it's hard to see where Joe might end up, but if he came to Arsenal I'd be quite happy with that.
"But I don't think that would be the position that Joe's looking for you know, to be in competition with someone. I think he wants to go to a club and be their number one."
Hart came under fire for his performances for England at Euro 2016, while he was criticised for a handful of errors during his time in Serie A, although he became a popular figure among Torino fans.
But Seaman, who earned 75 caps for the Three Lions, insists that Hart should remain number one under boss Gareth Southgate.
"For me, Joe is the number one by a long way," he said. "I know he's been away in Italy but the quality that Joe had before he went was fantastic.
"It's only a manager that had a problem with Joe's persona I suppose; it was nothing to do with talent. So for me, I was really happy that Joe went and was actually playing in a really competitive league, and then when he came back for England he still showed what he's got which was so satisfying to me.
"You know he took a big blow in the summer, not only with England but then for your manager to turn round and say that to you, that shows a lot of character, how he's reacted to that."