Carroll was a flop at Anfield and the Reds fear they could be conned again, because Sissoko's performance on Sunday for France was nothing like his half-hearted performances last season.
Newcastle were relegated, and the Frenchman was well below par.
Spanish newspaper Mundo Deportivo claims the Reds have made an £18million offer for the France international, which is more than either Arsenal or AC Milan have bid but Toon chiefs are now expected to demand almost double that amount on the back of the midfielder's exploits at Euro 2016.
Despite being relegated to the Championship, Rafael Benitez's side are claiming they have no intention of parting company with the 26-year-old unless the price is right.
Sissoko still has three years remaining on his current contract while other suitors include the Reds neighbours Everton and Premier League rivals Tottenham Hotspur.
Capped 44 times for France, he was snapped up from Toulouse in January 2013 for just £1.5million.