Cunha is viewed as an ideal addition to play in one of the two attacking midfield positions in Amorim’s preferred 3-4-2-1 formation.
Cunha – Wolves’ top scorer this season with 16 goals to his name in all competitions – plays in a similar system under current boss Vitor Pereira.
United are set to face competition from a number of Premier League clubs for Cunha, with Liverpool, Arsenal, Chelsea and Newcastle all known to be looking to sign a forward this summer.
Cunha has scored 32 times in 87 appearances for Wolves but his disciplinary record may be of some concern to suitors.
The former Atletico Madrid striker has been sent off twice this season, missing six games in total through suspension.
The forward said in an interview with the Observer in March that he has told Wolves he needs to “take the next step” and fight for titles.
United’s planning for next season is hindered by uncertainty over their financial situation.
At a conservative estimate, the club stand to gain around £100m in additional funds if they win this season’s Europa League and qualify for the Champions League.
But, with each league position worth £3m in the Premier League, United stand to lose around £24m should they finish in their current position of 14th compared to an eighth-placed finish last season.
Following Sunday’s home defeat by Wolves, Amorim said the club have a “plan” to improve the squad but that the situation could not be addressed until the summer.