United are reportedly considering whether to increase their offer, but it's unclear if Palace would even accept an improved £60 million.
United apparently see the England Under-21 international as a long-term replacement for Antonio Valencia, who will leave the club when his contract expires on June 30.
However, Palace seem to believe they have the upper hand in the negotiations. Wan-Bissaka has a contract with the Eagles until 2022 and has no intention of ditching the club in the summer.
"I am with Crystal Palace at the moment," he told the Guardian. "That is where my contract is and that is where I will be next season."
Wan-Bissaka emerged as a potential transfer target after an impressive 2018-19 campaign in which he ranked second and third, respectively, in interceptions and tackles among Premier League players.