Brendan Rodgers has urged Luis Suárez to repay the loyalty that Liverpool demonstrated throughout his racism and biting controversies as they prepare for a protracted dispute, potentially a legal one, with Arsenal over the striker's contract. The Liverpool manager delivered his message as he warned Arsenal to either swiftly meet the club's valuation of the player – set at more than £55m – or forget about a deal.

Suárez and his agent, Pere Guardiola, believe talks should commence on a prospective move to Arsenal now that Liverpool have received an offer of more than £40m – albeit by one pound – for the Uruguay international. Liverpool maintain that a clause in the contract Suárez signed last August obliges them only to consider a bid in excess of £40m and inform the player of developments. Real Madrid, set to bank £34.5m from the sale of Gonzalo Higuaín to Napoli, may yet formalise their interest in Liverpool's prized asset.

"If Arsenal want the player, then they have to produce the value for the player," Rodgers said. "There was an offer two weeks ago of £35m. Two weeks later it is now £40m and £1 – I don't think it is anywhere near what he is worth. But it is two-fold, really. A player may want to go but then somebody has to pay the value of that player. It is not something we want to run on too long. It is something that can't run on too long and [the end of] that period will come soon."

John W Henry, Liverpool's principal owner, underlined his club's view that Arsenal did not trigger a release clause in Suárez's contract with Tuesday's offer of £40,000,001 when he mocked the bid on Twitter. "What do you think they're smoking over there at Emirates?" he posted.

Mockery aside, Liverpool are angered it took Arsenal two weeks to improve their initial offer of £30m plus £5m in add-ons, and only then to a sum that their chief executive, Ivan Gazidis, had been told would be instantly rejected. For their part Arsenal, evidently encouraged to believe that £40,000,001 would prompt negotiations with Suárez, hope the 26-year-old will agitate for an exit from Anfield in the coming days. A Premier League or legal hearing could ultimately be required to resolve the stand-off should it continue.

Daniel Geey, a football lawyer at Field Fisher Waterhouse, said: "Premier League regulatory commissions have previously been tasked to look at such cases, as Liverpool know from the Christian Ziege ruling in 2002. The difficulty in the Luis Suárez case is that, even if it went as far as a regulatory commission or to court, and the judge made it clear what the clause says, that is not going to happen before this transfer window closes and perhaps not even before the January transfer window closes.

"Presumably Arsenal are not supposed to know about any confidential clauses in Suárez's contract. That was the problem for Liverpool in the Ziege case when they were fined for making an illegal approach after they were informed of a £5.5m release clause in Ziege's [Middlesbrough] contract. The commercial reality is that Luis Suárez may have to force Liverpool's hand or Arsenal will raise their offer. Liverpool are not going to force the issue in relation to a provision which they believe does not allow Suárez to speak to prospective suitors."

Rodgers was due to hold further talks with Suárez, and inform him of Arsenal's rejected second approach, after Liverpool's pre-season friendly over Melbourne Victory on Wednesday. The striker received a rousing reception from a remarkable crowd of 95,446 at the Melbourne Cricket Ground, where he appeared as a 72nd-minute substitute and created a late goal for Iago Aspas in a 2-0 win.

It was Suárez's first club appearance since receiving a 10-match ban for biting the Chelsea defender Branislav Ivanovic in April. Rodgers believes the support the striker received from Liverpool then, and throughout the Patrice Evra racism controversy that resulted in an eight-match suspension, should be reciprocated by a player who wants to join a club in the Champions League.

The Liverpool manager said: "The only talks there have been are between Luis and myself. There's no doubt the market nowadays is very small so Luis will always be linked with top clubs but I think the support he's received from the supporters and the people of the city of Liverpool has been unrivalled.

"In the period of time he's missed a lot of games for various reasons and the people have stood by him like a son and really looked after him. So I'm sure that, whatever happens in the coming weeks, that will be on his mind because it's certainly something you can never forget."

Rodgers added of Arsenal's interest: "It may be a distraction, but players are paid enough money now to produce for their clubs and he just has to keep his professionalism, which he has done."

The Liverpool goalkeeper José Reina, meanwhile, has passed a medical before a proposed season-long loan move to Napoli.