The Brazilian striker is a purple patch having scored six goals in his last five appearances.
Jesus scored four in a win over Watford last weekend
And Mills believes the club will put forward a new contract to the former Palmeiras man.
"I don't think he will be leaving this summer," Mills told TribalFootball.com, courtesy of FreeSuperTips.
"This talk and speculation was around last summer, his form wasn't great and he'd left out and I said at the start of the season that he'll still play 30+ games for Manchester City.
"Even if he isn't first choice right now, I don't think he's far off 50 game involvements this season so far.
"City will usually play around 60 games in a season with the cup runs and Champions League.
"I'm sure there will be things going on behind the scenes with his contract and there will be a few debates or games around it.
"He could leave or go play elsewhere and I think City will look at him and look at how well he's served the club.
Jesus after scoring against Real
"It'll come down to the value of money and where City values him at.
"What's the length of his next contract and how much is he worth; that'll be the next decision.
"He's been great for City, Pep's been great for him, and he's been great for Pep so I would be very surprised if there isn't an offer on the table for him shortly."
City paid £27m plus add-ons to sign Jesus from Palmeiras in January 2021.
Jesus has since scored 57 goals in 155 Premier League appearances.
He has also won three Premier League titles, an FA Cup and three League Cups.
The Brazil international has said he is focused solely on winning the Premier League and Champions League this season.
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!