The Sunday Mirror says the Merseyside club hope to wrap up a summer deal for the 19-year-old.
Delph was a revelation for Leeds last season and had scouts flocking to Elland Road to monitor his progress.
Manager Simon Grayson was determined to hold onto the Bradford-born midfielder, who emerged through their youth system.
But after failing to secure promotion from League One in the play-offs for the second successive term, he will reluctantly allow the player to leave.
However, Leeds are making it clear that unless their valuation is met, he will remain their player.