The 25-year-old Bosnian international has been in scintillating form for the Potters this season, attracting interest from a host of rival Premier League clubs.
Red Devils boss Sir Alex Ferguson is a long-term admirer of Begovic, and believes he is the right man to take over from under-fire first-team stopper David De Gea at Old Trafford.
However, Manchester United will now face competition for his signature, with Roberto Mancini keen to bring the former Portsmouth star - who moved to the Britannia Stadium for £3million in 2010 - to the Etihad, in a bid to keep Joe Hart on his toes.
Tony Pulis will be determined to keep Begovic beyond January, but may be forced to concede defeat, and sell the in-demand goalkeeper at the end of 2012/13.
Earlier this month, the Daily Telegraph valued the Stoke star at around £12million, with reports saying that Begovic was the most wanted goalkeeper in the country.
Chelsea offered £4million to take the player to Stamford Bridge, just six months after he signed for the Potters, but Pulis was quick to reject the Blues' offer, and reassure Begovic that he remained a big part of his first-team plans.