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."
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.
Keane, meanwhile, left United for Burnley in January 2015 but Mourinho is known to be eager to bring the 24-year-old defender back to Old Trafford.
The Portuguese views predecessor Louis van Gaal's decision to sell the centre-back for £2m as a mistake and believes his central defensive options are limited.
In theory, a 25% sell-on clause agreed at the time of that deal should bring the price down. However, Burnley manager Sean Dyche has said the Clarets have no financial need to sell Keane, who made his England debut in March.
Prior to the January transfer window, United showed interest in Benfica's Sweden centre-back Victor Lindelof, 22, while left-back is another area of weakness.
Earning Champions League football means United have avoided the potential loss of £50m in sponsorship income and prize money.
However, one senior club source said the forthcoming transfer window was likely to be "crazy", given the increased spending power within the Premier League as a result of the new £8.3bn TV deal and clubs such as Inter Milan and AC Milan willing to spend big to try to rediscover former glories.
A year ago, Mourinho marked his first summer at Old Trafford by bringing in striker Zlatan Ibrahimovic, defender Eric Bailly and midfielder Henrikh Mkhitaryan by the first week in July, before midfielder Paul Pogba re-signed from Juventus for a world record £89m in early August.
In December, BBC Sport was told the United manager felt he needed at least two more transfer windows to shape his squad.
Mourinho decided not to buy in January, but since then Ibrahimovic and defender Marcos Rojo have suffered cruciate knee-ligament injuries which will keep them out until next year and former Germany midfielder Bastian Schweinsteiger has left for Major League Soccer in the United States.
United went on to finish sixth in the Premier League which, apart from the disastrous campaign under David Moyes in 2013-14, was their lowest placing since 1991.
Manchester United are likely to limit their summer spending to three or four key signings.