Jesus is entering the final 12 months of his contract at the Etihad Stadium and has been linked with a move to Arsenal, after City's recent acquisitions of Erling Haaland and Argentine striker Julian Alvarez.
Real Madrid and Chelsea have shown an interest in the 25-year-old but Gilberto would like to see his fellow countryman move to north London.
When asked whether Arsenal would represent a good fit for him, Gilberto told talkSPORT: "If he goes to Arsenal, I do believe it's going to be a good move for him, also for Arsenal."
Gilberto spent six years at Arsenal between 2002 and 2008 and was part of the club's famous 'invincibles' team that went the entire 2003/04 league season unbeaten.
But seeing his former club slip below the standards set by the likes Thierry Henry, Patrick Vieira and Robert Pires, has left the 45-year old disappointed at the Gunners' plight.
"Do you know what's frustrating for all Arsenal fans? I think for me it was, they missed out the opportunity to be in the Champions League after a few years - four or five years if I'm not wrong?, " he said.
"Lets see, I think Arsenal need to get back to the top of the league over the main competition because it's so hard to see Arsenal in the last few years not playing in the Champions League and not fighting for the title.
"I know that compared to Man City and Liverpool they are not at the same level. Arsenal must work hard and work well to get back to the good times and start to sort the situation and compete for the title."
Gilberto also pointed to a lack of 'winning mentality' and feels that it was lost when Arsene Wenger stepped down as manager.
"During a transition sometimes you lose also the mentality. I think this is what is hard because they had the winning mentality and at some point it seems like you're losing this," he added.
"As we lost some points, you have to have people able to work with the players and to put them in the right mood, in the right way to think.
"Listen we are in one of the best clubs in the world it's not acceptable for us to do what we are doing. It's time for us to do what is right and do it with the right mentality according to what the club needs."