The 19-year-old German forward, who has scored five goals in 24 games this season, is highly regarded in his homeland, and many feel he has the technical ability to become one of the best players in Europe.
He could become the most expensive German player in history, should a deal be completed.
The chances of City completing a deal in the January transfer window appear remote given Schalke don’t want to sell and Manuel Pellegrini’s insistence that he doesn't need any reinforcements. It is hardly a surprise the Blues are monitoring his progress, though—City want young talent and Sane fits the bill.
“I think the squad is complete,” Pellegrini said recently. “As always, I said that we are not going to close the window but we are not really thinking of any special players to bring in.”
It was a typically coy response from the Chilean, but clearly it would take something hugely appealing to persuade him to sanction a deal this month.
And last month, per Bild (h/t Sam Lee of Goal), Schalke general manager Horst Heldt said: "We don't want to sell him and Leroy doesn't want to leave the club. Even Manchester City haven't got that much money!"
Sane is quick and likes to run at defenders—an exciting player with confidence beyond his years. Consistency has so far evaded him, but that’s hardly unusual for a young star. Almost every teenage footballer has periods where their form downturns. It’s how they react that is the most important thing.
Pep Guardiola, the Bayern Munich manager, was fairly effusive in his praise last year: "Leroy Sane is a huge talent. I can only congratulate Germany on having a talent like him"
Clearly, Sane is a young player who will attract attention from the best. If a deal can be done at the right price, most clubs in Europe would be tempted.
However, the development of Kelechi Iheanacho should be taken into account before any deal for Sane is pursued.
Iheanacho has played a total of just 275 minutes for City’s first team this season. His four goals from such slender opportunities speaks volumes about his ability and future chances of success.
He has everything. Quick feet and speed of thought. Vision and maturity. Technical quality and the confidence to try something spectacular.
City are desperate to start producing their own talent. Their City Football Academy (CFA), opened just over 12 months ago, cost them over £150 million and was a clear statement of their intent. Finding and developing their own world-class players is central to their future plans.
Iheanacho is the first one through who can consider himself a first-team squad member. There’s a desire to see him succeed, both among the players and the fans.
Pellegrini’s reluctance to play the 19-year-old more regularly is the only thing holding him back.
With Sergio Aguero’s injuries meaning he’s had his least effective season at the Etihad Stadium, and Wilfried Bony’s inability to transfer his Swansea form to the City side, it’s baffling Iheanacho has been given so few opportunities to impress.
Pellegrini doesn't see Iheanacho as an out-and-out striker, rather a withdrawn forward.
If Sane arrives, it can’t be to the detriment of Iheancho’s progress. Having the finest youth development facilities in the country is useless if the most talented young players aren't given an opportunity to show what they are capable of.
It's possible they could play together, but the fear is Iheanacho's progress is stunted further should another young, attack-minded player arrive.
Rob Pollard is Bleacher Report's lead Manchester City correspondent and will be following the club from a Manchester base throughout the 2015/16 season. All quotes were obtained firsthand unless otherwise noted. Follow him on Twitter @RobPollard_.