And Sterling would not automatically turn down a switch to Old Trafford if the opportunity arises.
The 29-year-old won four Premier League titles at the Etihad, one FA Cup and five EFL Cups during his stay with City.
Chelsea are open to including Sterling in a move for Jadon Sancho, who is set to leave United
But while he has maintains an affinity with his former club, playing for United - globally recognised as one of the biggest teams on the planet - is an option Sterling would give consideration too.
There is a pessimism about whether a deal that would see Sterling and Sancho swap clubs is possible.
Sterling’s reported £325,000-per-week wage will be problematic for all the clubs showing an interest ahead of Friday’s deadline.
Similarly, Sancho’s reported £300,000-per-week salary would not fit into Chelsea’s lowered wage structure.
Juventus also have a concrete interest in Sancho, with the Italian club believed to be more advanced in their move to sign the winger.
Juve, with Aston Villa and Crystal Palace, are also interested in Sterling.
Arsenal, over the weekend, were not actively pursuing Sterling but are fully aware of his situation. It remains to be seen if the Gunners change their stance ahead of Friday night’s cut-off.