He said: "I've not had the chance to get to know them personally or spend time with any of my team-mates up to now, but of course I know them from having played against them in the past".
Sanchez could feature for United on Friday alongside Pogba and Lukaku who are also in contention to play.
Armenia global winger Mkhitaryan, also 29, fell out of favour with United manager Mourinho after just 18 months at Old Trafford.
City in August past year came close to signing Sanchez and looked to be the favorite to get him this month, only to end their interest in the forward following a rival bid from United.
I must say I always gave 100%, until the last day, when I asked the manager to be in the team, because I wanted to make a contribution.
Sanchez also thanked the Arsenal fans for their support over the years before revealing it was a dream come true for him to join United when it appeared as if he was destined for Manchester City.
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In a statement issued by United, Sanchez said he had spent "three-and-a-half wonderful years" at Arsenal "and I bring with me very positive memories of that great club and its fans".
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Henrikh appeared 39 times for Manchester United, scoring five times and was part of their UEFA Europa League winning squad last season.
Wenger said: "Henrikh is a very complete player".
Mkhitaryan, who has scored once and contributed five assists in 15 Premier League appearances this season, joined United when Mourinho pipped Wenger to sign him.
The Sanchez-Mkhitaryan deal is the latest move of a January transfer window during which Liverpool sold Philippe Coutinho to Barcelona for 160 million euros and signed central defender Virgil Van Dijk from Southampton for £75 million (85.5 million euros).
Wenger told reporters: "We are not close to a deal for Aubameyang with Dortmund or anybody else".