The 28-year-old England international is valued at around £15million, having emerged as one of the finest left-backs in all of Europe.
Red Devils boss Sir Alex Ferguson is a long-term admirer of Baines, and is keen to bring him to Old Trafford to provide competition for vice-captain Patrice Evra.
However, United have been unwilling to pay Everton's valuation of the former Wigan star, who still has two-and-a-half years to run on his current deal at Goodison Park.
David Moyes is unlikely to sanction the sale of Baines in January, but the player is expected to be the subject of intense interest at the end of the season.
PSG have been credited with an interest in signing Chelsea's Ashley Cole - who is entering the final six months of his Stamford Bridge contract - but Carlo Ancelotti is also believed to be considering a bid for Baines.
Meanwhile, the Blues regard Everton's free-kick specialist as a potential successor to Cole in west London should the veteran defender head to the French capital next summer.