As with Cunha, Mbeumo's Premier League experience is viewed as a major positive as Amorim needs players who can hit the ground running as United look to make a more positive start to the season than their three sluggish efforts under Erik ten Hag.
Mbeumo scored a career-best 20 goals for Brentford last season, while he also contributed nine assists to the Bees' cause.
An international colleague of United goalkeeper Andre Onana, Mbeumo is likely to miss four weeks of the 2025-26 campaign because of Cameroon's participation in the Africa Cup of Nations in Morocco.
Cameroon play Gabon in their opening group game on 24 December.
The renewed move for Mbeumo comes as the future of Alejandro Garnacho is once again the subject of intense debate after he posted an image of himself wearing an Aston Villa shirt with the name 'Rashford' on his social media channels.
Fellow United outcast Marcus Rashford responded to the post with a 'my brother' message to the Argentina forward, who has been valued at £60m after being told by Amorim to find another club this summer.