Earl, 19, made his Preston debut in August and has featured 12 times in the Championship this term.
The two Premier League clubs are both closely following his development, according to The Sun.
Liverpool have struggled at left-back in recent years and Jurgen Klopp fancies strengthening in the position.
Meanwhile, Everton boss Sam Allardyce is on the hunt for Leighton Baines’ long-term successor.
Earl is currently sidelined after undergoing a minor operation on cartilage damage last month.
The Southport-born starlet is under contract with Preston until June 2020 after penning a three-year deal in September.
Speaking at the time, Lilywhites boss Alex Neil said: “Josh has been excellent, he’s been a real surprise for me because I didn’t really know anything about him.
“He played at Lancaster last year and came through the youth system and as soon as I saw him in the first couple of games I thought we had a cracker on our hands.
“I think for what he has done in the first team he has been rightly rewarded, he has all the attributes to become a top player for us going forward.”
Earl added: “I’m happy to sign it, it has all happened for me in the last few weeks and I can’t thank the gaffer enough for the opportunity he has given me.
“Obviously getting my first pro contract was a big thing for me but signing this new contract is a big moment for myself and my family and I’m happy with how I have done so far.
“I never expected all this to happen, the plan was to go on loan at the start of the season and get games but the opportunity came about here and I like to think I have taken it.
“The first four games I’ve played have been tough but slowly and surely I’m getting to grips with it.”
