The English newspaper also claimed that the Arsenal player has agreed terms on a lucrative four-and-a-half year contract worth £450,000 a week.
Although United's medical staff were with the team during their 1-0 victory at Turf Moor on Saturday afternoon, but were due to meet up with Sanchez after to put the player through his medical.
Speaking after the game, Jose Mourinho said about the deal: "It's so close, so close, so close."
"I'm positive, I know my people are doing everything, absolutely everything they can, the owners with the green light, Mr Woodward working hard, everybody is giving everything they can, and I think they will be successful."
Both Mkhitaryan and Sanchez have reportedly said their goodbyes on Friday, with the part-exchange deal set to be officially announced soon.
Arsenal don't appear to be missing their striker as the London club emphatically beat Crystal Palace 4-1 in their Premier League game on Saturday, with the Armenian midfielder set to join Arsene Wenger's side as part of the deal.