The 26-year-old Portugal international has fallen down the pecking order at Old Trafford after a bust up with United chief Sir Alex Ferguson and failing to secure a contract extension.
He is currently out of action with a hamstring injury but hasn’t played for the Red Devils since being substituted after a disappointing performance in the 3-1 Champions League victory at Braga in early November.
It has been a largely frustrating career for Nani at Old Trafford but he displayed the quality he possesses in an excellent 2010-2011 season where he scored nine goals and provided 18 assists in the league, helping United on their way to the title.
Wenger is keen to bolster his squad as his inconsistent side continue to fight on all fronts for glory this season. With the increasingly likely departure of Theo Walcott in January, Wenger could view Nani as an ideal replacement.
The winger is contracted to United until 2014 but it seems his relationship with Ferguson is becoming increasingly strained and that Nani has privately conceded his future lies elsewhere.
Zenit St Petersburg and Paris St Germain among others have been said to be interested in him but it is believed that he would prefer to stay in England, which will give Wenger hope if he is to pursue his interest in the player.