The 25-year-old looks to be stalling on the six-year contract the Potters have offered, with rumours starting to circulate that the defender wants to run down the remaining 18 months of his current deal at the Britannia Stadium.
Red Devils boss Sir Alex Ferguson is a long-term admirer of the England international, who was allowed to leave Old Trafford to join up with Stoke in a £1million deal in 2008.
However, Shawcross has been earning rave reviews this season, as Tony Pulis's side have gatecrashed the top half of the Premier League table, with the centre-back's fine individual performances attracting the attention of a number of clubs.
Roberto Mancini is another manager keeping tabs on the player's ongoing contract situation, with a view to enticing him to the Etihad Stadium in the New Year.
Joleon Lescott has fallen down the first-team pecking order, and has been linked with a move away from Manchester City, while Kolo Toure will be heading off for Africa Cup of Nations duty next month.
Manchester United have stronger central defensive options following the recent return of club captain Nemanja Vidic, but with Rio Ferdinand's long-term future far from certain, they too could still renew interest in Shawcross if he becomes available in January.