And this week the Bundesliga champions' manager, Niko Kovač, was forced to apologise after he made comments suggesting he was hopeful the former Schalke man would be joining the Bavarians.
City might well opt to cash in on the 23-year-old. With just two years remaining on his contract, his value will decrease over the next 12 months. Furthermore, he's no longer considered a key part of Pep Guardiola’s first-team.
It might be best for the Premier League champions to sell Sané and bring in someone more suited to what the City boss wants from his wide forwards. With less than a week before the summer transfer window closes for English clubs, Guardiola and the recruitment team at the Etihad don’t have long to get in a replacement if they do part ways with Sané.
Finding someone to fill the void left by the left-footed winger won’t be easy. Over the past two seasons, Sané has appeared in 4,289 minutes in the Premier League. During this time he’s averaged 0.52 assists – a number no other attacker in the English top-flight can match.
He’s averaging 0.39 open-play assists. Again, it’s a number that sees him ranked first in the league when looking at attackers.
His expected assists total of 0.31 sees him peerless in that category as well. On top of that, Sané is creating 0.52 big chances on a per 90-minute basis. Which is, as you guessed, the best once again.
He’s also ranked third for dribbles completed behind Eden Hazard and Wilfried Zaha. His ability to break lines and beat a man is vital for City. Even the sternest of Premier League defences struggle to contain him.
His average of 8.26 touches in the opposition’s penalty box is the third highest, this time behind Mohamed Salah and City team-mate, Raheem Sterling.
Sané is not just a creator, either. His 0.41 goals during this period put him in the top 20 among Premier League attackers.
He’s overperforming his expected goals (0.22) and that highlights he’s adding quality to his shots – his post-shot expected goals per 90 average being 0.31.
Despite all of this, though, there are players out there who could replace him in the City squad.
Mikel Oyarzabal is one name being mentioned and there's a detailed profile on the versatile Spaniard here. There are others and here we take a look at three possibilities, detailing why exactly they fit the bill.
According to reports, Barcelona want rid of the man they courted for the best part of 12 months. The Brazilian has failed to set the Camp Nou alight since his £140million move from Liverpool in January 2018. He's simply not the player he was during his time at Anfield.
It's understandable, however.
On Merseyside, the Brazilian wasn't competing with Lionel Messi. He could do Coutinho things without the pressure of getting in the way of arguably the best player to ever play the sport.
While he'd have to share the spotlight at the Etihad, he'd have a lot more freedom on the pitch than he does with Barcelona. He could rediscover his form. If he managed it, City would have another world-class talent at their disposal.
He's not as electric as Sané but he can slalom his way past opponents with great ease.
He's a creator and a goalscorer rolled into one. Coutinho is also capable of the spectacular, giving the team he's in that x-factor they wouldn't otherwise have.
At one stage last season, Werner was one of the most sought after players in Europe. Regularly linked with Liverpool and Bayern Munich, interest has died down over recent months with RB Leipzig seemingly not willing to sell their star striker yet.
Yet reports have emerged to suggest the Bundesliga side don't want to lose him on a free. With his deal expiring at the end of the 2019/20 season, now is the last chance for RBL to command a high fee for the German international.
City could swoop in and sign the versatile forward. He ticks a lot of boxes. Firstly, he can play a number of roles across the attack. He's a regular goal threat, finishing last season with 0.57 goals per 90, and he chips in with assists, too, 0.25 per 90.
He's not an elite dribbler, averaging just 2.88 per 90, but he is no stranger to carrying the ball and it's a skill that can be worked on if required.
He's explosively quick and a real chance-getter. Under Guardiola, he could be something special. He's got the traits needed to play alongside and in place of Sterling as well as leading the line to give Sergio Agüero a break here and there.
Remembered by many in England for his ill-fated time with Newcastle United, Thauvin has transformed into one of the most devastating wide forwards in Europe over recent seasons for Marseille.
His exploits in front of goal have seen him net 53 times over the past three seasons in Ligue 1 while assisting a further 27 more. Over that period he’s averaged 0.56 goals per 90 from an expected goals average of just 0.33.
Overperformances can be a red flag at times with players more often than not revert to the norm. However, given Thauvin has done this for three straight seasons it’s clear the Frenchman is part of the elite in the sense overperformance is now expected.
Still only 26, Thauvin is only just hitting his peak years. He might not feel as though a move to City is in the best interest for his development, he's a guaranteed starter for Marseille, but Sané did make 21 starts in the Premier League last season so there are enough minutes to go around.