The 25-year-old spent three years contracted to the Citizens between 2018 and 2021, but he never made a single senior appearance for the club.
Following a brief loan spell with Middlesbrough in 2018, Harrison spent three years on loan with Leeds before joining the club permanently last summer for around £11.5m.
Harrison has become a first-team regular for the West Yorkshire outfit and was a key player in helping the club avoid relegation from the Premier League last season, scoring eight goals in 35 top-flight appearances.
The Stoke-on-Trent-born winger has since been linked with a switch to Newcastle United, who have allegedly been priced out of a move for Bayer Leverkusen's Moussa Diaby.
According to the Manchester Evening News, Man City included a 20% sell-on clause in Harrison's deal when he joined Leeds.
It is thought that Harrison is now valued at around £35m by Leeds, meaning City could receive around £4.8m if the Whites agree to sell to winger to Newcastle or another interested club.
The Premier League champions previously included a similar clause in Jadon Sancho's deal when he joined Borussia Dortmund, and they eventually earned around £11m when the winger made his big-money move to Manchester United last summer.
Leeds head coach Jesse Marsch was recently questioned about Harrison's future at Elland Road, and claimed that clubs have been keeping tabs on the 25-year-old for some time.
Speaking to reporters on Saturday while on their pre-season tour in Australia, Marsch said: "There's always been interest in Jack, like many of our players. But I know that Jack is also very happy here and that he's done really good, that he's a big part of what we're doing.
"Of course there's always possibilities that big transfer offers come in and clubs then have to decide how it fits and what are the best options moving forward. But, for me, Jack Harrison is a big part of our plans moving forward and we're counting on him this season, for sure."
While Leeds have made close to £100m from the sales of star duo Raphinha and Kalvin Phillips, Man City have already made around £135m in players sales this summer, including the big-money departures of Gabriel Jesus and Raheem Sterling to Arsenal and Chelsea respectively.
They have also sold a number of highly-rated youngsters including Gavin Bazunu and Romeo Lavia to Southampton and Darko Gyabi to Leeds.
City could also make up to £30m from the potential sale of Oleksandr Zinchenko, who is seemingly edging closer to joining Arsenal.