In demand: Bryan Mbeumo
The Cameroon forward has been the subject of two rejected bids from Manchester United, with the Red Devils’ most recent offer worth £62.5million.
It has also been claimed that Tottenham hold an interest in the winger, with former Brentford boss Thomas Frank taking up the north London vacancy after the sacking of Ange Postecoglou.
Standard Sport previously reported that Mbeumo wants to make the move to Old Trafford, and has told the higher authorities at the Gtech Stadium of his wish.
Giles issued an update on Mbeumo’s situation on Monday, telling BBC Sport that “not so much” progress had been made on a deal for their talisman.
He even went as far as saying that there was a likelihood that Mbeumo would stay put in west London should potential suitors not present an acceptable offer for his services.
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"He had a fantastic season," Giles said. "We expected big interest in him, we have had big interest in him.
"He has his ideas about where he wants to take his career. He is well within his rights to do that.
"It is not impossible he is still a Brentford player next season if we agree he is going to stay."
"Any club will tell you that if it's not the right deal, why would we do it?
"He is certainly one of our best players, if not our best player, and we need our best players. There's no harm in keeping your best players."