The 26-year-old French international has been in scintillating form in La Liga this season, and has attracted the attention of a number of major European clubs.
Red Devils boss Sir Alex Ferguson is keen to bolster his defensive options, after injury ruled out club captain Nemanja Vidic for the remainder of the season.
However, the reigning Barclays Premier League champions will now face competition from PSG, with Spanish newspaper Superdeporte reporting that the Ligue 1 giants have entered the race for his signature.
Valencia are looking for at least £20million for the talented defender - and PSG are prepared to splash the cash as they look to provide recently appointed manager Carlo Ancelotti with the tools to oversee a French revolution.
Manchester United on the other hand, may be put off by the inflated valuation, but if Ferguson is serious about signing Rami, then he may be forced to part with some serious money.