Luiz is out of contract at the end of this month having signed an initial 12-month deal when joining from Chelsea in an £8 million transfer last summer.
ESPN reported in May that Arteta was keen for the Brazil international to remain part of the squad, a view he publicly stated for the first time when speaking ahead of the Gunners' trip to Manchester City on Wednesday evening.
"I'm really happy with David," he said. "I want to keep him here with us. He's been a key role model for me since I joined. I like what he produces on the pitch. I like his influence around the players and the club. I'd love to keep him."
Arsenal are currently expected to retain Luiz given they have an option for a second season but any agreement is likely to be influenced by wider financial difficulties resulting from the coronavirus pandemic.
The Gunners are the only Premier League club to have negotiated a wage cut rather than a deferral -- 12.5% for 12 months. Luiz earns £120,000 a week and it is currently unclear whether he would be asked to renew on a lower wage.
Arsenal resume their league campaign at the Etihad Stadium on Wednesday evening five points adrift of fifth-placed Manchester United and facing an uphill battle to secure Champions League qualification for the first time since 2017.
The Gunners are understood to be prioritising loan and swap deals in the market this summer and Arteta underlined the difference Champions League football could make to his future plans, having previously claimed prior to the coronavirus outbreak that the club were strategising "two or three different scenarios" regarding transfers depending on budgets.
"The fact that we've not been in the Champions League for the past three seasons has put an enormous amount of pressure on the club in financial terms," he said.
"We know our responsibility and the aims -- and how much that would relax the financial position that we are in. But we have to go game by game. It is not achievable in one or two games. It's a process over 11 games that we have. We know the target, the difficulty of the task because there are a lot of clubs in that fight. We have to give it a go and believe that we can do it.
"We are trying to put a plan together to improve what we have. We haven't been able to achieve the goals we have wanted in the last three years and there is a reason behind it.
"If we stand still that gap will become bigger and bigger. I haven't come here to accept that. The challenge for us is to improve the players we already have and find ways to improve the squad in the right positions to give us the best possible chance to compete at that level. It's getting higher and higher every year."