The Whites want to bolster their midfield options this month after letting Mateusz Klich leave for MLS side DC United.
Several options have been looked at, but Leeds are now trying to grow the American contingent at Elland Road.
They want United States midfielder McKennie, who is on the books at Italian giants Juventus.
Leeds have put an agreement on personal terms in place with McKennie, but now must try to find common ground with Juventus in terms of a fee.
They will be hoping they can do so quickly, with McKennie also attracting attention from other clubs.
If McKennie moves to Leeds then he will link up with countrymen Brenden Aaronson, Tyler Adams and Whites boss Jesse Marsch.
With the clock ticking down on the transfer window, Leeds will want to push a move for McKennie over the line soon.