Italian journalist Matteo Moretto told Radio Marca that Liverpool had already entered talks with Wharton, 22, ahead of the summer transfer window.
The England international is expected to leave Selhurst Park after a season that has included a Europa League semi-final run with Crystal Palace and a place in England's World Cup squad.
United had identified Wharton as a priority midfield target as they plan for a significant summer rebuild. With Casemiro set to depart and Manuel Ugarte's future also unclear, the addition of a modern, progressive central midfielder ranks among the club's most pressing requirements.
Palace, however, will not sell cheaply. Reports indicate the south London club are demanding a minimum of £80 million. Wharton still has three years remaining on his contract and holds significant leverage.
The player himself was asked about the mounting speculation on Thursday, ahead of Palace's Conference League semi-final first leg against Shakhtar Donetsk, which he played the full 90 minutes of.
"Obviously the praise is good and being linked with big clubs is obviously a compliment in a way," Wharton said. "I don't really pay attention to it. I know that I'm doing well. The coach will tell me. The outside ones, I don't really focus on. I just try to focus on myself."
Liverpool's interest centres partly on their own midfield situation. Curtis Jones is out of contract in 2027, and Alexis Mac Allister has shown inconsistency at points this season. Wharton's range of passing and composure on the ball have been identified as qualities Slot's system does not currently have in sufficient depth.
Real Madrid are also monitoring the situation, with the prospect of a strong World Cup pushing Wharton's value upward over the coming weeks. That dynamic suits neither United nor Liverpool, both of whom would prefer to move early.
For United, losing this particular race would be a significant blow. The club made Wharton their primary midfield target ahead of this summer and Carrick's coaching staff have been tracking him closely. Whether Liverpool's reported head start in negotiations proves decisive will depend on Palace's appetite to deal, and on which club Wharton ultimately chooses.