Arsenal reportedly wanted Luke Shaw as part of a deal for Alexis Sanchez.
The Chilean is set to complete his move to Manchester United with Henrikh Mkhitaryan moving in the opposite direction.
Both Sanchez and Mkhitaryan will undergo medicals on Sunday after an agreement was reached between the two clubs.
It had been reported that Arsenal had made an enquiry about Anthony Martial but the Sun reports Shaw was actually wanted.
The left-back is out of contract in the summer but United turned down the approach.
They are expected to take up the option of the extra year on his contract after he worked his way back into Jose Mourinho's plans.
Shaw had started United's previous five games but was left out for Ashley Young for the win at Burnley on Saturday.
Ahead of the clash, Mourinho explained his decision.
"I'm really happy with Luke. I don't need to go to the transfer market to get a left-back because I'm really happy with Luke and with the adaptation of Ashley Young so I’m really happy," he said.
"But I think this match is a very specific one and one that you need the experience of Young and he also projects very well in attack.
"That's a decision [you make] when you have two players and a good squad, and you can adapt."