The No2 will follow Klopp out of the club at the end of the season.
But pundit Alan Brazil told talkSPORT: "I am told the players wouldn't mind the number two, Pep taking over."
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Former Liverpool striker Dean Saunders added: "I heard that as well. At least Lijnders knows what's going on there.
"It's difficult, who do you give the job to? That club is that big."
Lijnders has been with the Reds since 2014, though had a year away in charge of NEC Nijemegen.