The Red Devils kicked off their summer spending by bringing in Joshua Zirkzee from Bologna last weekend, and they then confirmed Leny Yoro's signature from Lille on Thursday night.
Man United are also determined to bring in a new central midfielder this summer, and Ugarte is believed to have been identified as the club's leading target in that area of the field.
According to transfer expert Fabrizio Romano, the 20-time English champions have come to an agreement with Ugarte over personal terms.
Romano claims that the Uruguay international is keen to make the move to Old Trafford even though the Red Devils will not play in the Champions League during the 2024-25 campaign.
Man United 'agree' personal terms with Ugarte
Discussions between Man United and PSG are said to be continuing over a fee, but a number of other clubs are also believed to have expressed an interest in signing him this summer.
Ugarte arrived in Paris from Sporting Lisbon last year, and he turned out for Luis Enrique's side on 37 occasions in all competitions, providing three assists in the process.
The midfielder enjoyed a strong Copa America fo Uruguay this summer, meanwhile, contributing heavily to his side finishing third at the competition.
Journalist Florian Plettenberg has said that Ugarte wants to join Man United "with immediate effect", with the South American determined to complete a move to the English giants.
Will McTominay, Casemiro be sold by Man United?
Both Scott McTominay and Casemiro are being linked with moves away from Old Trafford this summer, and it is likely that at least one will depart during the current window.
McTominay is currently being linked with Fulham and Tottenham Hotspur, while Galatasaray are also believed to have expressed an interest in securing his signature.
Casemiro continues to be linked with a move to Saudi Arabia, although there is not believed to be anything imminent when it comes to a possible switch for the Brazilian.
Christian Eriksen is also expected to be allowed to leave for the right price, while Hannibal Mejbri is not believed to be in Erik ten Hag's plans for the 2024-25 campaign.
Man United were heavily linked with Benfica's Joao Neves earlier this summer, but the Red Devils have now cooled their interest, and the Portugal international could potentially head to PSG as Ugarte's replacement.