The 33-year-old's existing agreement expires on June 30 having only signed a one-year contract when joining the club from Chelsea in an £8 million deal last summer.
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The Gunners have an option to sign him for another year but a decision has not yet been taken and Luiz's case was not helped by a calamitous performance in Wednesday's 3-0 defeat to Manchester City at the Etihad Stadium.
After being dropped from the starting lineup, Luiz came on as a first-half substitute for an injured Pablo Mari, made a mistake for the opening goal and was then sent off for conceding a penalty which Kevin De Bruyne converted.
His appearance lasted 25 minutes. Afterwards, Luiz decided to conduct a live television interview in which he expressed his regret that his contract situation has not been resolved before now.
For players whose contracts expire this summer, the deadline to extend for the end of the 2019-20 season is June 23.
And Joorabchian hinted in an interview with talkSPORT on Thursday morning that the delay is linked to ongoing contractual negotiations with several other players including Mari, Cedric Soares, Bukayo Saka and Pierre-Emerick Aubameyang, who are about to enter the final year of their deals.
"The situation from Arsenal's point of view will be resolved this week," he said. "I think it's just not Luiz's situation. There are several issues within the whole structure that will get resolved. June 23 is the deadline for most of the clubs to renew their contracts so that they can finish the season off and beyond. So irrespective of any situation, by June 23 everyone's situation should be resolved.
"The contract situation has dragged on not because of any reason, not because of the will of David or Arsenal to finalise but really the situation that has occurred with this pandemic.
"And as I have repeatedly said all through the pandemic, at the moment the most important thing is to get football back, not to talk about contracts, futures etc.
"Now it becomes a moment where you have got 14 days left, you are at a critical point in your career where you have probably got three, four, five years left at the very top level, it is in the back of your mind.
"But that's not an excuse of yesterday's performance. He also said 'I'm not using this as any excuse.' They played one of the best teams in England and Arsenal's lack of shots on goal and lack of control of the game would have put pressure on the defence and with no excuse whatsoever, David wanted a different type of game."
Speaking at a news conference on Thursday, Arsenal coach Mikel Arteta defended Luiz despite his poor showing in Wednesday's match.
"We need to be fair on him. Me personally I am going to defend him with everything I have because I believe in him. He has shown me a lot of things in his time here and his career speaks for itself," said Arteta.
However, the Gunners boss added that the club will make decisions regarding its roster amid the coronavirus pandemic that halted play across the league for three months.
The club is also waiting for results of further tests but fears are growing that Mari could miss the rest of the season with ankle injury.
"Well we cannot forget the financial situation. The way that COVID-19 has hit every club and the economy in general, it's going to have an impact," Arteta said. "What the club is doing at the moment is assessing the situation and trying to clarify a lot of uncertainties that we have in the future.
"We have to make big decisions and time-wise it is difficult to fit them in with our needs. We are trying our best and the club is trying their best. It is difficult sometimes because it puts the player or our sporting necessities in a difficult situation.
"Again, we have to adapt. It is what it is. That is why I wanted to protect David yesterday. That is why I did not start him. But it's a funny game and after 20 minutes you need him, a player who has had a lot of uncertainty in the last few weeks."