As the Red Devils seem to be in pole position to sign Sanchez in the January transfer window, it was reported that Henrikh Mkhitaryan had been offered to Arsenal as part of a potential swap deal for the Chilean forward.
In addition, Mkhitaryan was left out of the United squad for their 3-0 win over Stoke City on Monday (15 January) as Mourinho admitted pre-match that his decision was not a tactical one.
Following the win, the United boss revealed that there was a possibility of the Armenian international leaving Old Trafford.
"He is our player so I can speak about him," Mourinho stated as he further fuelled rumours. "He has a lot to give us. Is he going to be involved in one deal leaving us? It is possible.
"But it is also possible he stays. But I'm just trying to protect him. The market is open."
Speaking about Mourinho's decision to leave Mkhitaryan out of the squad, Neville believes it is a clear indication that a deal for Sanchez is close and that the 54-year-old manager would be completely fine with a swap deal.
"The clearest sign that something's happening with Sanchez is that Mkhitaryan isn't playing, that he's not in the squad and Jose was happy to volunteer that information to us," Neville told Sky Sports via FourFourTwo.
"He wanted to keep the player clear, saying that he does rate him but I think he'd happily swap him in any deal for Alexis Sanchez. Anybody would."
As for Mkhitaryan, Neville adds that he is clearly a talented player but lacks the consistency to truly be a star player for United, having lost his place in the starting eleven.
"He's a talented player but you have to have more than talent," Neville explained. "He's shown glimpses that make you think he's coming but then he goes missing."