The signing of another playmaker at Anfield has been mooted for some time.
The Reds are expected to explore the options available to them, with it suggested that interest could be rekindled in World Cup winner Fekir a year on from passing on a deal.
Mellor is not convinced that the Frenchman is needed, however, with others capable of filling his role, but he does believes that fresh faces at left-back and up front are required.
“He’s done very well for Lyon,” the former Liverpool striker told AmericanGambler.com of Fekir.
“He scored a very important goal for them to progress through the Champions League group stages this season.
“He’s an attacking midfield player who contributes goals.
“There wasn’t too much pressure on the midfield to score goals last season because the front three scored so many again.
“Alex Oxlade-Chamberlain is perhaps that player, when fit, who can get goals from midfield.
“There is no doubt Nabil has the quality but it’s whether he can come into what is already a very competitive area within the Liverpool squad.”
Mellor added on the positions he would like to see addressed: “So many players always get linked with Liverpool, that’s always the way it is.
“What I would say is that [Alberto] Moreno and [Daniel] Sturridge leaving Liverpool means more coverage needed in those positions, a left full-back for [Andy] Robertston who has been outstanding, and perhaps he may look at depth with Daniel Sturridge leaving as a striker.
“One to eleven, Liverpool are outstanding. There’s no doubt about that. There’s more to come from [Naby] Keita,[Adam] Lallana, and Oxlade-Chamberlain in those midfield positions, Fabinho has settled in.
“You look at Liverpool’s squad and it is really strong, and I don’t think Jurgen will dip into the market unless he thinks someone could add even more quality, but Liverpool are in a position where they can attract pretty much any player in the market because of how they have performed.
“They’re now in a position to compete for the top trophies in the game.
“When you look at the homecoming for the Champions League, there were a million fans in the streets, which shows the support for the club.
“I think players around the world would have seen that and want to be a part of that if they’re lucky enough to be selected by the recruitment or Jurgen Klopp.”