The former French international has been looking for a new team since being sacked by Marseille and banned by UEFA earlier this season following an altercation with a supporter.
However, Evra is hoping to turn things around by returning to the Premier League under David Moyes, who briefly managed him during the player's eight-year stint at Manchester United.
The 36-year-old was spotted arriving at the Rush Green training complex on Wednesday morning ahead of completing a medical and finalising his free transfer to the club.
'Sky Sports' also reported that fellow Premier League side Everton are interested in the left-back's signature too, but that he would prefer a move to London over Merseyside.
If the deal becomes official, it would ease Moyes' squad troubles going into the second-half of the season as he is currently dealing with a significant casaulty list.
With Evra, the former United manager would be guaranteed experience as the defender made 379 appearances during his nine seasons in Manchester, winning five Premier League titles, three League Cups and the Champions League.