The 32-year-old, who has made 333 appearances for Man City, will close the curtain on a nine-year spell at the Etihad Stadium when the season comes to an end this weekend.
As Zabaleta ponders his future, the Evening Standard believes that the Hammers have offered him a two-year contract as Slaven Bilic looks to reinforce his defensive options this summer.
"If you link him to West Ham, which seems to be the case at present, he'd be absolutely perfect," Hammers stalwart Brooking told BBC Sport.
"He can play a few different roles, but more than anything, the West Ham team have lacked leaders. When things have gone a little bit dodgy during a game and you're looking around for who is going to get hold of it and put a couple of tackles in - Zabaleta would be perfect for this group of players at the club.
"Whoever he ends up with, he's going to be a plus. I'd be delighted [if he joined West Ham]."
Zabaleta has won five trophies during his time at Man City, including two Premier League titles and the FA Cup.