Manchester United's latest offer of £62.5 million was not deemed sufficient by Brentford to convince them to sell the 25-year-old player.
It is understood that Mbeumo has already expressed his desire to join Manchester United and has asked his current club to facilitate a transfer.
Manchester United is not the only club interested in Mbeumo. Tottenham has also held talks with Brentford about a potential move, with the possibility of a reunion between Mbeumo and his former manager, Thomas Frank.
Brentford is reportedly open to letting go of the Cameroon international, who scored 20 Premier League goals in 38 games during the previous season.