The two clubs have held talks, and Mbeumo is said to prefer a move to Old Trafford despite added interest from Tottenham, who have appointed his former boss, Thomas Frank.
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Sky Sports News understands Brentford want in excess of £65m for Mbeumo and United have so far offered a package rising to £62.5m.
Speaking exclusively to Sky Sports News, Giles explained that there is a deal to be done, however, it must be “right” for Brentford.
“There is significant interest in Bryan. His current preference has been well publicised, ” Giles said.
“He had an unbelievable season and we expected interest in him. From what I understand, he is also, if needs be, happy to stay at Brentford next year as well.
“We’ve spoken to Bryan and his representatives. It’s not a given that he’s going to depart this summer.
“If we get the right offer, there is the potential for a deal to be done but there is only so much we can say now on that.”
Sky Sports to show 215 live PL games from next season
From next season, Sky Sports’ Premier League coverage will increase from 128 matches to at least 215 games exclusively live.
And 80 per cent of all televised Premier League games next season are on Sky Sports.
