Liverpool have already been told that their No1 target to replace Arne Slot would be open to joining.
Slot is facing significant pressure just six months after winning the Premier League title, having lost seven of their last eight top-flight games.
Wednesday's 4-1 home loss to PSV in the Champions League has raised further concerns, but within the club it remains business as usual for the time being.
It was claimed earlier this month that Julian Nagelsmann was the man most wanted at Anfield should Slot be sacked, but the coach's commitments to Germany ahead of next summer's World Cup makes a move a likely non-starter.
That has prompted links with Luis Enrique, whose Paris Saint-Germain team knocked Liverpool out of the Champions League last season en route to winning the competition for the first time.
The Mirror claim that club executive have discussed a succession plan should Slot be sacked, but fear Enrique may may wait until the end of the season before taking a new job.
The Sun add that club legend Jurgen Klopp could be drafted in for the rest of the season, but Enrique takes over. Klopp is currently Global Head of Soccer for Red Bull.
But Liverpool will feel confident the Enrique would be interested in a move to Anfield, having previously spoken of his desire to manage one of the Premier League's top sides.
"I follow above all the Premier [League] because I would like to go to England to work," Cadena Ser radio in 2023
"I wouldn't go to any team but to one that could do important things, which greatly reduces the number. I don't put my hopes up, really, because there are many candidates."
He added: "I am lucky because my personal life fills me up," he said. "That it takes longer, that no offers arrive, well, it is what it is. I would go to a team with possibilities."
