Suarez's adviser Per Guardiola met both manager Brendan Rodgers and chief executive Iain Eyre to speak about the unsettled star.
Arsenal have made a high-level approach to the club's American owners and been rejected. But the interest remains.
However Guardiola assured Liverpool that Suarez will not rock the boat and is willing to wait to see if any buyer reaches the magic £40 million figure for him.
Suarez is on holiday after a busy spell with his national team and will miss the start of the season as he serves a ban for biting.
But the future of the striker could be settled sooner if the right offer is made, although
Arsenal are well short of the valuation.
After the round of talks Liverpool are relaxed about what happens next as Suarez and Guardiola will quietly test the market and see if there is a giant bid - or if he stays.