Although United have been strongly linked with Chelsea forward Nicolas Jackson and Aston Villa goalkeeper Emiliano Martinez in recent days, it has always been the priority at Old Trafford to get the Mbeumo deal done in time for Amorim to work with him in the Chicago, where United will largely be based for their 13-day trip.
The 25-year-old scored 20 Premier League goals last season and a number of clubs were interested in him, including Tottenham, now managed by former Brentford boss Thomas Frank.
However, Mbeumo’s preference was to join United.
Brentford’s other main goal threat, striker Yoane Wissa, is the subject of interest from Newcastle.
Last season Amorim repeatedly spoke about United’s failure to convert their chances.
Their 44 Premier League goals was their worst return in a domestic campaign since they were relegated in 1973-74.
United have signed forward Matheus Cunha and defender Diego Leon in the summer transfer window.