Rumors have emerged in recent days that Pep Guardiola's men are preparing to tempt Arsenal with an offer for the 21-year-old.
Saka was arguably Arsenal's best player last season, scoring 11 goals and providing seven assists in 38 Premier League appearances as the Gunners finished in fifth place.
Walcott reckons Saka is more likely to win trophies with Manchester City but his playing time will be reduced at the Etihad Stadium and has urged him to stay put with Mikel Arteta's side.
“Obviously, when Manchester City coming knocking on the door, it is such a hard thing for any player really to turn down," Walcott told talkSPORT.
"He is very young, but I feel that he likes the area of London Arsenal are in, the fans have been fantastic - and at the Emirates, which is one of the best stadiums I have ever played in.
"He has great support, and I will be intrigued. My heart says he will be at Arsenal next season."
"He needs to understand that the playing opportunities will be limited at Manchester City.
"He will, of course, be more likely to win things, but that's not to say Arsenal won’t win things. I think they are in that phase, they are slowly starting to get there. They would have taken fifth at the start of the season, given how it went.
"I am hopeful he will be at Arsenal next season, I am pretty sure of that."
