Despite the presence of his former Bees manager Thomas Frank now at Spurs, Cameroon international Mbeumo still favours a move to United this summer.
However, after United's last offer rising to £60m, Spurs have now tabled a bigger bid of £65m plus £5m in add-ons, says the Mirror.
On the wages side, United have offered terms reaching £200,000-a-week, including bonuses, while Tottenham's package totals £130-140,000-a-week.
Frank's opinion clear
For Frank, he's made it no secret that he'd like to continue working with Mbeumo, stating late, last season: "I'm the head coach. I want my best players to stay forever. 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 that 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.
"But I'm very happy he's here, and I'm convinced that Bryan will still be happy playing football here."