The newspaper revealed on their website that the north London club have been eager to renew both Ozil and team mate Alexis Sanchez' contracts and are close to finalising one of those.
Arsene Wenger raised eyebrows last week when he said it was an "ideal situation" having players in their final year at the club.
The Sun has revealed that the 28-year-old has indicated to the club that he is ready to agree terms for a stunning £225,000-a-week wage deal.
The Sun claims Arsenal believe a breakthrough has been made in the club's quest to tie Ozil down to a new £225k-a-week deal, with the World Cup victor reportedly giving the impression that he's ready to put pen to paper.
Kelechi Iheanacho Leicester throws his boot down after he is injured during the preseason friendly against Borussia Moenchengladbach
The report also claims that Ozil's agents have been trying to find him a move, but with no luck, which means he will now stay with the Gunners.
Unlike with Sanchez, who has been heavily linked with Paris Saint-Germain, Manchester City and Chelsea, Ozil doesn't appear to have been the subject of any great interest from suitors.
The Chile global had rejected an initial offer believed to be worth £225,000-a-week but the Gunners now plan to make Sanchez the highest paid player in the Premier League. Creating high wages like Ozil's potential new earnings can create problems with other players questioning why they aren't worth the funds.
Carragher expects Conte to leave Chelsea in next 12 months
They're not scared to get rid of them and they have a big say in how that club's run. Since Abramovich came in I think they've won more trophies than anyone.