Many are of the opinion that Jurgen Klopp should be looking to bring in another playmaker.
Since the departure of Philippe Coutinho to Barcelona in the winter transfer window of 2018, creativity in the middle of the park at Anfield has been lacking.
That was expected to be addressed this summer, with it suggested that interest could be rekindled in Fekir.
Liverpool came close to landing the France international 12 months ago, only for medical concerns to see them walk away from a deal.
It could be that a fresh approach is made for the talented 25-year-old, but Barnes is not convinced that he is required.
The Reds legend told The Sport Review when quizzed on the links to Fekir: “Yes, he’d be a good addition to the squad.
“But, it’s going to be difficult to get into the front three.
“If you look at the way Xherdan Shaqiri played, he could feature as one of the midfield three as well.
“It’s always good to have quality to help the squad. But it’s pure speculation until it happens.
“I don’t necessarily feel that Liverpool are desperate to sign anybody because of the squad they have and with two new players coming back in terms of Alex Oxlade-Chamberlain and Joe Gomez, who didn’t feature last year. We’ve still got Adam Lallana.
“It could be good for the squad but I don’t think we’re desperate to sign anybody.”
Fekir shone for Lyon again during the 2018-19 campaign.
He contributed 12 goals and nine assists to the cause of an exciting young squad.
The door has been opened for him to make a move this summer, with a mass exodus of talent on the cards at a leading Ligue 1 club.
Lyon president Jean-Michel Aulas has said of Fekir: "His preference is towards a departure.
“We are open to discussions. We have no news.
“We are waiting for proposals in the coming days but, for the moment, we do not have any.”