Fekir could yet make a post-World Cup move to Liverpool with almost two months of the transfer window still to go.
Barnes says he and fans should support Klopp whatever the decision is with regards to prising Fekir away from Lyon.
"If they feel that there is a medical issue then they shouldn’t [sign him]," Barnes told the Daily Star.
"Liverpool have to do what they think is right and Jurgen Klopp has to make those decisions.
Liverpool transfer news: Nabil Fekir move claim made by Anfield hero John Barnes (Image: GETTY)
Liverpool transfer news: Nabil Fekir move claim made by Anfield hero John Barnes (Image: GETTY)
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"Obviously, we trust Jurgen Klopp and the choices he makes so if Jurgen Klopp decides not to sign him then we shouldn’t no.
"If he decides to sign him with his slight injury but it’s not an injury that’s going to stop him playing and we feel it’s worth it then I’ll back him."
Fekir has been talked of as a long-awaited replacement for Philippe Coutinho, who quit Liverpool for Barcelona in January.
However, former Liverpool ace Paul Ince seems to think his old side can do without a successor to the Brazilian playmaker.
Nabil Fekir to Liverpool is now 50/50 says expert
"Coutinho was the one that everyone thought when he has gone, that it is it, [they are finished]," said Ince.
"I don’t know whether Klopp felt the same, but I felt that losing Coutinho was the best thing that could happen for Liverpool because they were so dependent on Coutinho, everyone was talking about Coutinho.
"Once he left it was then time for the players to step up and say: ‘Well now we have got responsibility.
"'It is not a one-man team as everyone was saying. We will show that it is not.'"