The Catalans drafted in the Frenchman to replace Neymar in 2017.
They paid around £90m up front with performance related bonuses included in the deal.
However, according to Spanish daily Marca, the £35m bonus payment must be paid in full if he is sold before 2022.
Roberto Firmino is misfiring this season and the Reds have been linked with Dembele.
Barca boss Ernesto Valverde dropped Dembele from his match-day squad for Barca’s recent clash with Real Betis on November 10.
The France star missed training with a stomach bug although reports suggested he had fallen out with Valverde.
Despite rumours of a rift between player and manager, his form has been solid.
The attacker has netted six goals and chipped in with two assists in all competitions.
Dembele’s agent – Moussa Sissoko – has vociferously denied claims his client is looking for a move.
“There is no doubt about his future at all,” Sissoko said.
“Ousmane continues to work, he is in a big club and Valverde loves him, and he is also in the national team and (Didier) Deschamps continues to trust him.”
Pundit Craig Burley says neither party should rush into a deal.
“I don’t think there is a rush to sign him at the moment no,” Burley said.
“Neither is there a rush to sell him, yet.”
Jurgen Klopp already has other strikers at his disposal.
Daniel Sturridge, Divock Origi and Dominic Solanke are all waiting in the wings.
Out of the trio, Sturridge has been the most impressive understudy for Firmino in recent weeks.
The England international’s season now runs the risk of being derailed with an FA charge relating to breaches of its betting rules though.
Klopp has also been linked with Borussia Dortmund sensation Christian Pulisic.
He knows the USA international well having managed him at Dortmund and has repeatedly been tipped to snare him.
He is reported to have made an £11m bid to bring Pulisic to Anfield in August 2016.