The Red Devils are looking to bolster their attack after a humiliating 2024-25 campaign, finishing 15th in the Premier League and losing the Europa League final.
They have identified Mbeumo as an ideal option, who scored 20 goals and provided eight assists in 38 Premier League appearances last season.
The 25-year-old has only a year left on his contract at the Gtech Community Stadium, but Brentford have the option to extend by another 12 months.
Tottenham Hotspur, Newcastle United and Arsenal have also been linked, but Mbeumo has informed the Bees he only wants to join United.
Their second proposal at £55m and £7.5m of bonuses was expected to be enough, but that has also been turned down.
However, talks continue between the two clubs and there is confidence a transfer can be completed soon.
United reportedly have the funds available for signing Mbeumo without requiring sales in advance.
But they want to avoid overpaying for players in the market, a mistake they have been making over the previous years.
