United have already seen two bids rejected for the Cameroon international-the latest understood to be worth up to 62.5 million euros - and Mbeumo has reportedly informed the west London club of his desire to make the move.
But Brentford are in no rush to sell. Speaking to BBC Sport on Monday, Giles confirmed that the Bees are in "constant dialogue" with the 25-year-old and suggested that a stay at the Gtech Community Stadium remains on the table.
"He had a fantastic season. We expected big interest in him, we have had big interest in him," Giles said. "He has his ideas about where he wants to take his career-he is well within his rights to do that.
It's not impossible he is still a Brentford player next season if we agree he is going to stay."
Mbeumo, who netted 10 goals in 25 Premier League appearances last season, has emerged as one of Brentford's most valuable assets, particularly in the absence of Ivan Toney during his suspension. His versatility across the front line and ability to influence big games has made him a key target for United as they look to reshape their attacking options.
Still, Brentford are clear: any transfer must be on their terms.
"He is certainly one of our best players - if not our best player - and we need our best players," added Giles. "There's no harm in keeping your best players. If it's not the right deal, why would we do it?"
Arsenal have confirmed the signing of Spanish goalkeeper Kepa Arrizabalaga on a three-year contract, seven years after he joined Chelsea in what was then a world-record transfer for a goalkeeper.
Former Chelsea wonderkid Charly Musonda has announced his retirement from professional football at the age of 28.
James McAtee's future at Manchester City is increasingly uncertain, with reports that Bundesliga giants Borussia Dortmund and Bayer Leverkusen are among the clubs showing serious interest in the 22-year-old midfielder.
Former Liverpool manager Jurgen Klopp has called the club's reported fee for German midfielder Florian Wirtz "insane," warning that such massive transfers bring heightened expectations and pressure for both player and club.
