The Brazilian centre-back arrived in a surprise move from Chelsea last summer.
He has enjoyed an up and down season, but manager Mikel Arteta wants to keep him for another year, albeit on reduced terms.
Luiz, 33, currently earns £130,000-a-week.
But he may have to settle for a deal that is based on bonuses and incentives, rather than a higher outright salary, according to The Mirror.
It is all because of the financial constraints on the club, both due to COVID-19 and another likely year out of the Champions League.
Luiz's agent, Kia Joorabachian, remains confident that a club can be sorted.
He told Sky Sports: "He's very happy at Arsenal. He has an extremely good relationship with both the coach and the sporting director.
"He has good relationships all throughout the club, right up to the owner. He respects everybody.
"Arsenal had an option, which expired. We also had a pandemic [coronavirus]. So the option expired in the middle of the pandemic.
"We are all very aware of that situation and we are all trying, very slowly, to get back to this 'new normal'.
"These contract situations, these renewals, if he stays or if he goes... will all sort themselves out when we get back to some kind of 'new normal'.
"David will sit down with Arsenal before the season begins, have his conversations and they will both decide if he will stay or not. That will come before the season starts.
"The chances are very high [of Luiz being at Arsenal next season]. There is no desire to leave."