The 19-year-old was very impressive in the Championship on loan with Preston last season.
He is back with Villa, and wants to go through pre-season with Steven Gerrard's side.
Reports in Scotland state that Rangers are in the running for Archer, but Preston boss Ryan Lowe stated that he was told the player would consider coming back to his club if he does not get game time at Villa.
Lowe said, via the Daily Record: "If he becomes available, he's basically told me there's only one place he'd like to go and that's back here - so that is a big plus for us.
"I told him there is going to be loads spoken about him, loads of people throwing loads of money at Aston Villa to try and buy him.
"I don't think it is the right thing to do, for Aston Villa to sell him, I've already mentioned that to Stevie (Gerrard).
"But I think if he goes out on loan to us again next season, he will find his feet, find his level and kick on the following year."