United are interested in signing a right-back and a centre-back this summer with Trippier and Varane among the players on a list of targets drawn up by the recruitment department and manager Ole Gunnar Solskjaer.
Trippier is keen to return to the Premier League after two seasons at Atletico Madrid to be closer to his family but the price being quoted by intermediaries is more than £30 million, which United consider to be too much for a 30-year-old with very little sell-on value.
Solskjaer already has a regular right-back in Aaron Wan-Bissaka -- who cost £50m from Crystal Palace in 2019 -- and when Alex Telles was signed last summer as competition for Luke Shaw at left-back, the Brazilian cost around £15m from Porto.
Sources have told ESPN that Atletico are not willing to listen to any offers for Trippier as coach Diego Simeone considers him to be a key member of the squad, and doesn't have enough faith in backup option Sime Vrsaljko.
Varane has been a long-term target for United but interest this summer is being driven by his contract situation at Real Madrid.
The Frenchman has one year left on his existing deal and there is a feeling in Spain that he is keen for a new challenge, although sources have told ESPN he has not informed Madrid he has already decided against agreeing fresh terms.
The situation has been further complicated by Sergio Ramos' exit and should Varane also depart, it would leave the Spanish giants having to replace their first-choice centre-half pairing.
United have been made aware that even a year away from becoming a free agent, Madrid still value Varane at more than £70m. Sources have told ESPN that, as things stand, United do not hold an interest in Ramos.
United are willing to spend to strengthen the squad this summer but, according to sources, there are fears at Old Trafford that clubs in Europe are ramping up their prices for Premier League sides because of a view they are among only a few who can afford to pay transfer fees after the devastating financial impact of the coronavirus pandemic.
Information from ESPN's Eduardo Fernandez-Abascal was also included in this report.