Britain's Mirror newspaper said Sanchez was due to arrive in Manchester with agent Fernando Felicevich, with a medical scheduled for Sunday afternoon, while Sky reported that Mkhitaryan would have a medical in London.
The Mirror said the deals may not be officially completed until Monday as both Sanchez and Mkhitaryan are non-EU players and must have their work permits ratified by their new clubs.
Chile's Sanchez, 29, is set to become United's best-paid player, with some reports putting his salary at 400,000 ($554,000) per week, prompting a warning from former England boss Steve McClaren that his high wages could create dressing-room disharmony.
Arsenal boss Arsene Wenger and United manager Jose Mourinho both said they expected the two-way deal between the Premier League rivals to go through.
Wenger said Sanchez was absent from the Arsenal squad on Saturday because he was close to completing a deal that has been in the making since United out-bid Manchester City for the former Barcelona star.
"I expect soon or never," Mourinho said after his side's 1-0 win against Burnley. "I think it is so close, so close, so close that if it doesn't happen it's not going to happen."
McClaren, who was Alex Ferguson's assistant when Manchester United won the treble in 1999, said the Sanchez signing would be a major coup for the club but warned his earnings could unsettle other players.
"Wage parity is very important to players. Yes, they find out -- at all levels -- and if someone is paid a lot higher than others that can cause a problem," he said.
"If he (Sanchez) is on the wages that is being bandied about then other players will know that when their contracts come up or they are in demand from other clubs," he added.
"Any manager worth his salt would love to have Sanchez in their team," McClaren told BBC Radio 5 Live.
"Sanchez coming in for the second half of the season at Manchester United is a huge boost to them.
"He has got that experience and toughness, he wins games and he is a leader. It will lift the level of the whole club.
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