United appear to be in pole position to sign soon-to-be free agent Sanchez from Arsenal in January following reports that runaway Premier League leaders Manchester City pulled out of the running on Monday.
Mkhitaryan has been touted as a possible makeweight in a deal for the Chile international and talk of an imminent deal intensified after the United attacker was left out of the squad for the club's 3-0 win over Stoke City.
"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.
"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.
Speaking about Mkhitaryan — who has fallen out of United's line-up — Neville added: "He's a talented player but you have to have more than talent.
"He's shown glimpses that make you think he's coming, but then he goes missing."
Reigning Premier League champions Chelsea have reportedly entered the race to sign Sanchez from their London rivals, adding another wrinkle to the transfer saga.
"Apparently City have pulled out of the race to sign Sanchez, but I genuinely thought he was their player," Neville continued.
"Even this morning it was quite clear to me he was City's player.
"I still don't believe they've pulled out. Now Chelsea have come in, it's moving quickly and the next couple of days will be interesting."