United will be in the Champions League and boss Jose Mourinho said executive vice-chairman Ed Woodward has had his targets “for more than two months”.
Mourinho wants to enhance his forward and defensive options to challenge for the Premier League title next season.
United have been linked with Atletico Madrid striker Antoine Griezmann and Burnley centre-back Michael Keane.
“Ed Woodward has my list,” the Portuguese manager said after his side beat Ajax to win the Europa League for the first time on Wednesday.
“Now it’s up to him and the owners.”
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Griezmann has a 100m euro release clause in his contract and the 26-year-old France international said earlier this week that his chances of joining United were “six out of 10”.
Since then, a major stumbling block has been removed by United securing the return of Champions League football. They will go straight into the group stage after their victory over Ajax in Stockholm.
Griezmann has the pace and trickery United lack but, should a move falter, Torino forward Andrea Belotti is another option. The 23-year-old Italy international has scored 25 goals in Serie A this season.