Gradi has been given the green light by Reds boss Gerard Houllier and is trying to persuade Mellor to move to Gresty Road.
"I have spoken to Gerard Houllier and he has given me permission to talk to Neil about coming here on loan next season," Gradi told the club website.
"We're optimistic we can bring him here and that is a massive boost because we couldn't afford to sign a player of Neil's quality.
"He would be an ideal signing for us and would fit the mould very well. He is a young man who is eager to improve.
"He is just up our street, the right age, talented and very ambitious."
The 21-year-old has been a prolific scorer in the reserves but has had limited first team chances at Anfield.
He spent time on loan at West Ham last term, but that did not go to plan and he would hope for more from Crewe should he join Gradi's side.
Gradi, meanwhile, is also hoping to tie up a permanent deal for Manchester United goalkeeper Ben Williams, who impressed while on loan at the end of last season.
