Danish international Sorensen looks likely to leave the Potters after losing his first team place to Asmir Begovic last season.
City have just sold Shay Given to Aston Villa are in the hunt for an experienced keeper to provide competition for Hart.
With Champions League football coming to Eastlands this season boss Roberto Mancini wants a dependable backup keeper to step in if anything happens to Hart.
Stoke are also entering Europe this season as they prepare to tackle the Europa League and want Sorensen to stay and fight for his place.
The Dane – who played against City in the FA Cup final in May – has been in talks over extending his deal at the Britannia Stadium.
However it is thought that he will leave if he doesn’t feel there will be a fair fight for the number one jersey.
Whilst a move to Manchester would cosign him to the bench for a majority of the season a chance to play in the Champions League and challenge for trophies could be enough to lure Sorensen to City.
He would be available for a nominal fee and would certainly provide trustworthy competition with over 450 appearances in 12 years playing in the top flight for Sunderland, Villa and Stoke.