The 26-year-old has hit the ground running and is United's top scorer with four goals, netting in the win over Liverpool at Anfield and then scoring a brace a week later against Brighton.
Frank predicted Mbeumo will go on to achieve big things at Old Trafford, even if he hopes that is paused when his Tottenham side host United on Saturday.
"Of course I'll step out of my role at Tottenham. When you work with a player for six years, you get a close relationship. To see him develop from being a young man, 19-year-old when he moved to London and Brentford and left six years later, going into one of the biggest clubs in the world with all that focus and the way he stepped up.
"For me, looking from the outside, maybe a little bit biased, I think he's been their best offensive player.
"He can create, he can score, he works hard, he's a team player. He's the perfect example, in my opinion, for a player what I call about attitude, confident but humble. He's a top player.
"I think he will have fantastic success there. I hope that for him, not tomorrow, but in general I hope and wish him all the best."
"Right now they are in a moment where they have more or less every key player available and he's found his team, played more or less the same team in the last four or five games," Frank said.
"We know exactly what to expect from them. I think they have an incredibly dangerous front three. They're starting to get more up to pace and we need to close them down.