A report in The Mirror on Sunday suggested The Reds are prepared to let the Uruguayan leave in the January transfer window after he had "confided in friends that he remains determined to quit".
Arsenal had two bids for the striker turned down last transfer window, but The Mirror claims he will not be heading to north London but to La Liga, with Real Madrid the main target.
But a source in Anfield has denied the report, insisting Suarez has three years left on his contract.
"There could be no new contractual arrangement with Suarez once the season got underway and he was in dispute with the club, trying to push through a move,” BT Sport quotes the Anfield source as saying.
"However, that has all changed now and the club have made it clear that Suarez has three years left on his contract – well, just under now – and to be fair to the player he has shown his commitment on the field.
"What happens next largely depends on the club and player sitting down to discuss his future in the summer when he has two years remaining on his contract, and it is traditional at that stage for clubs and players to want to re-negotiate contracts.
"We shall all see how it unfolds in the summer when those talks take place. In the meantime, the manager has stated that Suarez will be treated the same as every other player under contract."