Sterling has joined Arsenal on-loan from Chelsea.
And Anderson told PA Sport: "It is going to be difficult because clearly Manchester City are the team to beat.
“But Raheem Sterling has come in on loan until the end of the season, and he is a really good player who can turn games.
“The manager’s signings have been good and I like what I see at Arsenal, so they have got a chance of bridging that gap (to City).”
Anderson, in his role as supporter of Prostate Cancer UK, also stated: “You could say Arsenal need a centre forward like (Erling) Haaland who is going to score them 20-odd league goals, but Kai Havertz has started quite well.
“So if he can continue to get in the positions to score the goals, and is up there with 15 or 16, maybe even 20, then you are going to be thereabouts.
“With the likes of Sterling, (Bukayo) Saka and Gabriel (Magalhaes) at the back, Arsenal have got some really good players, so it is going to be close.”