Old Trafford wish: Bryan Mbeumo wants to join Manchester United from Brentford this summer
The offer falls short of what Brentford would accept, however, and talks are set to continue over the coming days.
Mbeumo, who is keen on a move to United this summer, has one year left on his current contract, but Brentford have the option to extend it by another 12 months.
The Cameroon international enjoyed a brilliant campaign this season, scoring 20 Premier League goals and laying on seven assists.
Manchester United have already bolstered their attack by signing Matheus Cunha from Wolves for over £60m, but head coach Ruben Amorim wants further additions.
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It may take a similar fee to land Mbeumo, while United must also agree personal terms with the winger and some reports claim he wants £250,000 a week.
Brentford boss Thomas Frank confirmed last month that the club could sell Mbeumo this summer, but warned that he would not come cheap.
“I’m the head coach, I want my best players to stay forever,” Frank told Sky Sports News.
“I know that Bryan is very happy being here at Brentford, he’s thriving, doing well and playing fantastic. What happens in the future? I don’t know.
“I’ve said many times: we are a selling club. But at the same time we have to reinforce that there are 10 clubs in the world who aren’t selling clubs.
“So, of course, if the right price - and that’s going to be expensive - is coming, then I’m sure the club will be open for it.