The 21-year-old Englishman is out of contract in a matter of weeks and with talks stalling over a new deal to keep him at Goodison Park, the Reds are ready to pounce, with Bournemouth also interested.
Garbutt has been on the Everton bench in the Premier League 20 times this season and has made just four appearances in the top flight.
But he is highly regarded by the Toffees and a move to Liverpool would certainly cause a stir on Merseyside.
Roberto Martinez came under pressure after Everton’s game at West Ham on Saturday after he decided to play Brendan Galloway at left-back ahead of Garbutt, with Leighton Baines out injured.
Martinez said that decision was made just 90 minutes before kickoff and was based solely on footballing reasons, but it is looking increasingly likely that Garbutt will move on after six years with Everton.
Liverpool are expected to make numerous changes to their squad this season, and signing Garbutt on a free could be one of their early moves.
Would Luke Garbutt be a good signing for Liverpool? How important is he to Everton?