Whether Liverpool do actually go back in for a player they have previously shown concern about remains to be seen.
Talks were set to continue after the tournament but Liverpool pulled the plug.
Lyon have told Nabil Fekir to make a decision on his future by the turn of the year.
President Jean-Michel Aulas is renowned for being a stubborn businessman but now does not want to risk losing the player for cheap as his contract runs down.
That means that going into the January window, Fekir has just 18 months left on his current deal and that may allow Jurgen Klopp to drive the price down in the mid-season window; just like he wanted to during the summer.
Of course, the Frenchman returned from his summer excursions as a world champion but the Ligue 1 side did not tie him down to an extended deal.
Despite most in-the-know journalists suggesting that Liverpool will not reignite their interest in the 2018 World Cup victor, the rumour fires continue to burn, with some still convinced Jurgen Klopp is still keen to add one more attacking player to his team.
It appears as thought Fekir and Lyon are having issues over who is representing the midfielder.
"The sorting out of certain things regarding the question of his agent is underway. The aim, is to have a clear and precise position from his point of view between now and the end of the year", Aulas said, as quoted by the Liverpool Echo. "Jean-Pierre Bernes is still his agent, but he might not be between now and the end of his contract".