The Frenchman, who moved to Old Trafford alongside Nemanja Vidic in January 2006, will reportedly look to secure a move away from the club as he would not be willing to be back up to Baines.
PSG and Monaco were both said to be interested in making a move for Evra earlier this summer - particularly when it looked like Baines was closing in on a move to Manchester United.
However it now seems like the England international will stay at Goodison Park until January, at least.
Evra, 32, is still a mainstay in Manchester United's starting line-up - having started all three of the Premier League's competitive fixtures thus far.
However if Baines was to sign, Evra would ask to leave the club as he looks to nail down a starting spot in the France national team for next summer's World Cup in Brazil.