The Gunners are understood to have had a £42.5million bid accepted by the Spanish giants - but rumours on Monday morning suggested Manchester United had entered the race.
The Red Devils swiftly denied making contact with Ozil's representatives - despite seemingly lacking creativity during the disappointing 1-0 defeat to Liverpool on Sunday.
As a result, it now appears that the main challenge to Arsenal's hopes of bringing the 24-year-old to Emirates Stadium will come in the form of French champions Paris Saint-Germain.
Gunners boss Arsene Wenger said in the aftermath of Sunday's 1-0 victory over Tottenham: "It is a little bit like a domino game. Maybe something will happen in the last 24 hours, maybe not. It is very difficult to predict, but maybe we can surprise you."
Ozil, 24, signed for Real from Werder Bremen in 2010 in a deal worth around 15m euros but may find his chances of first-team football at the Bernabeu limited by Gareth Bale's world-record signing.
Although reports in Spain suggest Ozil is unfazed by the Welshman's arrival and remains determined to stay on and fight for his place, Real manager Carlo Ancelotti has appeared to welcome approaches.