The Cameroon international has seen two bids rejected by the Bees, though has made it clear he wants to move to Old Trafford.
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United have now submitted a third offer of £70m in the last 24 hours and are expecting good news from Brentford today, says the Mirror.
Mbeumo has already agreed personal terms with United and could inherit his favoured No19 shirt number, which has been vacant since Raphael Varane's departure last year.
Mbeumo currently wears the No19 shirt with the Bees, where he scored 20 Premier League goals last season.