While Mourinho and Arsene Wenger expect the move to be completed in the coming days, the Arsenal boss has stressed that the deal is dependent on Mkhitaryan also agreeing terms at the Emirates Stadium.
"It's so close, so close, so close," Mourinho told reporters after his side's 1-0 win at Burnley. "I'm positive, I know my people are doing everything, absolutely everything they can.
"The owners [have given] the green light, Mr Woodward is working hard, everybody is giving everything they can, and I think they will be successful."
Wenger, speaking after Arsenal's comprehensive 4-1 win at home to Crystal Palace, added: "I expect it to happen, but I can't announce it. In the next 48 hours, it will be decided. Until it's over the line, you can't say it will happen.
"It happens only one way, if the other [deal] happens as well. That's why it takes longer as well because it is coordinated."
Sanchez is expected to be offered a four-and-a-half-year deal at Old Trafford worth £450,000 a week - the highest wage of any player in the Premier League.