The Italian club has agreed to increase their offer for the 20-year-old French international striker to pounds 22m from pounds 18m, but that is dependent on Anelka agreeing to take a cut of pounds 4m in wages over the five years of his contract in Rome.
Arsenal's manager, Arsene Wenger, has left Anelka with no room to manoeuvre and, after last night's 1-1 draw with Monaco, he told Channel 5: "We wait until tomorrow midday. If there's no decision tomorrow morning then he has to come back [to Arsenal]."
Wenger had put the ball in Anelka's court earlier when he said: "We've agreed a fee with the club and now it's up to Nicolas whether he wants to join them. After that he will no longer be up for sale."
Lazio and Arsenal had previously failed to agree on a price for Anelka with the Italians failing to meet the London club's asking price, but now the onus is on Anelka to break the deadlock.
The player's agent, Marc Roget, said: "We have yet to reach an agreement on Nicolas' personal terms because Lazio have decided they want to pay him pounds 4m less. But I am hopeful I can persuade Nicolas to accept the new package and that a deal can be concluded."
Even if Anelka does agree to the salary cut, he will still earn a reported pounds 14m over five years - pounds 56,000 a week. Lazio have also asked his agents to cut their fee.
Another variation on the bizarre story being reported last night was that Lazio and Juventus, who had also expressed interest in Anelka, would share the burden of his fee and wages. Lazio would take him for two years, with Juventus then having the option to buy him, sell him on or take him on loan.
Arsenal's England goalkeeper, David Seaman, limped off the field as Arsenal were held to a lacklustre 1-1 draw away to Wenger's former club, Monaco last night.
With Tony Adams already set to miss the start of the season because of a hernia operation, the Gunners will not want also to be without Seaman, who had to be helped off the pitch at the end of the match with what looked like a pulled calf muscle.