Frenchman Remy is in Boston where he has undergone a medical with Brendan Rodgers' side ahead of finalising an £8.5million transfer to Anfield.
And it is understood that Deeney is the man that Harry Redknapp wants to replace the former Marseille forward, but it is thought they face competition for the 26-year-old’s services from Leicester. Burnley have also been linked with Deeney, though not at the £8million price tag.
Giuseppe Sannino's side seem reluctant to part ways with their top scorer who netted 25 times last season and as yet no club has met Watford’s valuation of the player.
With speculation mounting over an imminent transfer away from Vicarage Road, Deeney made a cheeky post from his official account on social networking site Twitter on Friday.
He tweeted: "Just to check with the people congratulating me on my move…Where have I gone and how much for?? I need to tell my mom the good news."
Burnley boss Sean Dyche told Sky Sports News that they cannot afford Deeney if Watford are demanding £8million.
"I don't know what club we are! There must have been a financial bypass with linking us with someone for £8million," he said.
"He's amongst many players I admire, good players. But we've got a certain brief from the club that we have to work to. The club has a base to build from, financially. We can't entertain £8m players, I can assure you of that."
Meanwhile, Adel Taarabt’s exit from QPR looks inevitable after he was left out of the club's pre-season tour to Germany.
Taarabt does not feature in Redknapp's plans for the new season and has been linked with a permanent transfer to AC Milan where he spent the second half of last season on loan.
Milan vice-chairman Adriano Galliani has said that a move is possible but has indicated manager Filippo Inzaghi’s preference is to sign a left-footed attacker.
QPR have also been linked with a move for Mathieu Valbuena but that deal seems unlikely as his agent is thought to be drumming up interest in the France international from clubs across Europe.