The England international has been strongly linked with a switch to Old Trafford in recent weeks, with the Red Devils believed to be keen to sign competition for Aaron Wan-Bissaka at right-back.
Atletico Madrid are said to be holding firm on their €40m (£34m) valuation of the 30-year-old, which is a figure that Man United are not prepared to pay in the current market.
According to Marca, Atletico are calm about the future of Trippier, who has a contract at Wanda Metropolitano until June 2023.
However, the report claims that Man United are refusing to give up on their pursuit of the defender and 'continue to lurk in the background', with the club still hoping to sign him before the transfer deadline.
Trippier, who is now back in training with Atletico following his involvement in Euro 2020, has provided 11 assists in 68 appearances for Diego Simeone's side in all competitions.