Manchester United midfielder Mkhitaryan, 28, will undergo a medical at the Emirates imminently after the transfer deal, details of the deal have not been disclosed, was completed on Saturday.
Sky Sports reported that the deal will be a straight swap.
Sanchez was missing from the squad for Arsenal's 4-1 win over Crystal Palace on Saturday wil reports saying he was on his way to Manchester.
""I didn't take him because there is a question of him moving to Manchester United and you cannot drive up north and play football at the same time," said Wenger.
United boss Jose Mourinho said the deal was "close" following his side's 1-0 win at Burnley on Saturday.
"In this moment there is no competition for places, we have four attacking players for three positions, three are starting, one is on the bench," said the Portuguese..
"You look to the attacking areas and we need that extra competitive internal competition but more solutions for us so let's see."
United signed Mkhitaryan, 28, ahead of Arsenal when the player moved to Old Trafford club for £26.3m from Borussia Dortmund in the summer of 2016.
The Armenian international has played 63 times for United, scoring 13 goals while Sanchez has scored 80 goals in 166 games for Arsenal since arriving from Barcelona for £35m in July 2014.