Talks of a fresh contract for the England international have been going on for quite some time, but the two parties are believed to be at loggerheads over the player's wages. It has been claimed in the past that the 28-year-old wishes to be paid £120,000-a-week, which would supposedly put him on par with the club's second-tier earners such as Nicolas Anelka, Michael Ballack and Michael Essien.
With Cole's contract with the Stamford Bridge outfit expiring in June, it is said that Red Devils' boss Sir Alex Ferguson - who is an admirer of the creative midfielder - has been alerted to the potential availability of the player.
It is claimed that the Scot is looking for a suitable replacement for Ryan Giggs, 36, and sees the Blues' midfielder as an able successor to the Welsh veteran.
If Cole should indeed let his contract run out and become a free agent, there will be no lack of suitors for him as Manchester City, Tottenham Hotspur and Serie A giants Milan have all been linked with moves for the England international.