The 24-year-old midfielder has been heavily linked with a move away from Juventus before the end of the window next week.
Juventus are open to selling him and Leeds have a clear edge in the race to sign him despite interest from a few other Premier League clubs.
Jesse Marsch and Tyler Adams have spoken with their American compatriot and Leeds have also agreed personal terms on a contract with McKennie.
But an agreement with Juventus is still missing and according to Italian outlet Tutto Mercato, they have a price in mind.
It has been claimed that Juventus value McKennie at €30m and want that figure before agreeing to sell him.
Juventus are open to letting him go but are insistent that they are not desperate to offload the American.
The Italian giants are also reportedly reluctant to drop their asking price to facilitate his departure.
It remains to be seen whether Leeds decide to reach that figure in order to get their hands on McKennie.