The newspaper claims the Spaniard has been monitoring Clarke's progress since the latter signed his first professional contract at Leeds last year.
The 18-year-old made his United debut earlier this season, under a man Guardiola once claimed to be the world's best coach - Marcelo Bielsa.
And he provided his first senior assist on Saturday, enabling Pablo Hernandez to settle the Yorkshire derby at Sheffield United.
But with Clarke under contract until 2021, not to mention Leeds being on course for automatic promotion, could the Whites really cash in when the transfer window re-opens?
This is what the Elland Road faithful are saying on Twitter...
Man City were previously interested before he signed a new contract with Leeds (until June 2021).— Daryl (@DarylRS29) December 4, 2018
Tenuous link from The Sun at best.
Plus he'll be a PL winger next season regardless. #lufc https://t.co/hhMSD0Ty0F
Personally can't see this happening. Mainly because Bielsa wouldn't bring someone into his lean squad, to teach them his way of playing to then offload them. And I imagine Pep has far too much respect for Bielsa to try poach Clarke. #lufc https://t.co/uEq3chaQeT— Jo Bedford (@El_Loco_JoJo) December 4, 2018
Not surprised. The lad is going to be world class.— Diddlysquat (@markrikko) December 4, 2018
Hands off Jack Clarke.— Steve Austin (@Steve_Austin33) December 4, 2018
Why on earth would we sell him tho? pic.twitter.com/ISUjfg6Ite— Reehan Gulamhussein (@ReehanG28) December 4, 2018
I am not liking the rumours of Man City lining up a bid for Jack Clarke in January #lufc— Mr T (@Leedsmatt) December 4, 2018
Another 1 they’ll ruin ♂️— Leitchy (@SS6_LUFC) December 4, 2018
150k a week.— Mr T (@Leedsmatt) December 4, 2018
It didn't take much for Byram and Taylor to have their heads turned by low profile Prem clubs. Man City will be a big draw to him.— Mr T (@Leedsmatt) December 4, 2018
He’s not good enough for city imo— (@Betting21mil) December 4, 2018
He’d be loaned out to a side worse than Leeds so it would be pointless imo— (@Betting21mil) December 4, 2018
According to the Sun, Manchester City are not the only Premier League club keen on Clarke.
The City winger, Brahim Diaz, has been strongly linked with a move to Real Madrid this week.