McKennie is a player Juventus are looking to offload before the end of the January transfer window and the clock is ticking.
The American has attracted interest from several Premier League clubs over the last few weeks but his future remains unresolved.
Leeds have held initial talks with Juventus over a potential deal to take McKennie to Elland Road in the ongoing transfer and it is claimed they have an agreement on personal terms.
But Leeds could face competition from Arsenal as, according to Italian daily Corriere dello Sport, the Gunners have probed about the possibility of signing him.
Mikel Arteta has already signed Leandro Trossard and Jakub Kiwior this month but wants to add another midfielder to his squad.
Arsenal have an interest in signing Eduardo Camavinga on loan but Real Madrid are unlikely to play ball.
The Gunners are looking at other targets and McKennie has emerged as a potential target for the club.
But Arsenal have only made an enquiry and Leeds are hoping to use their American connection to tempt McKennie into moving to west Yorkshire before the end of the window.