Mbeumo is said to prefer a move to Old Trafford despite added interest from Tottenham as a move away from the Bees looks increasingly likely. United submitted an improved bid in excess of £60Mfor the forward but Brentford rejected the offer which they see as too low.
The Cameroon international contributed 20 goals and eight assists in the Premier League last season, United see him as the player that can improve their toothless attack ahead of next season where manager Ruben Amorim will be hoping for more than 44 goals in the Premier League like last season.
However, speaking to BBC Sport, Giles explained that a deal for the forward would only happen if a deal is right for the club and there is a possibility that he could stay at Brentford if United to not up their bid.
"There's not so much (progress with Mbeumo). He had a fantastic season, 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, of course he does - 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.
"It has to be the right deal for Brentford, any club will tell you that. If it's not 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."
Giles also spoke to Sky Sports and again confirmed that Mbeumo leaving is not certain despite interest from United and Tottenham as Brentford try to get the best deal possible this summer.
"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."