Even before Loris Karius' costly errors in the Champions League final, Jürgen Klopp had been said to be looking at bringing in a new goalkeeper, with AS Roma's Brazilian worldwide Alisson most frequently linked with a transfer to Anfield.
The Reds have been heavily linked with a move for the Brazil No 1.
It's also said in the report Liverpool have little chance of landing Jan Oblak from Atletico Madrid, while alternatives, including Cologne's Timo Horn and Southampton's Alex McCarthy, are also out of reach at this juncture.
Fekir suffered a serious knee injury playing for France three years ago, and it seems the problem has hampered Jurgen Klopp's bid to get the transfer sealed before the World Cup.
Before the Champions League final - and Loris Karius' blunders - reports anticipated that the Liverpool boss would keep his compatriot as the club's number one stopper, and now those claims are being made again. Roma may not have been the most defensively sound side in Serie A last season, but so often he was on hand to get them out of trouble with some inspired goalkeeping.
That last piece of the club's new midfield still needs filling though, and with news of a move for West Ham's Manuel Lanzini having been scuppered by an injury sustained on worldwide duty, the shortlist narrows by the day.
Last summer, Mohamed Salah signed for the Reds in what must be one of the biggest bargains the Premier League has ever seen.
Some wouldn't want the club to be quite so careful.