The Spanish giants are thought to have accepted a £42.5m bid and sources at a hospital in Germany claim Ozil is already undergoing a Gunners medical there.
The 24-year-old, who joined Real in 2010 from Werder Bremen for 15m euros, is set to become the first through the Bernabeu exit door following the world record-breaking arrival of Gareth Bale from Tottenham.
Gunners boss Arsene Wenger said in the aftermath of Sunday's 1-0 victory over Spurs: "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."
Reports earlier on Monday suggested Manchester United may launch a last-gasp attempt to hijack the move, having looked toothless going forward during a lacklustre 1-0 defeat at Liverpool on Sunday.
However, with the Red Devils rubbishing those reports and despite additional interest from French champions Paris St Germain, it appears increasingly likely that Arsenal manager Wenger is on the brink of his first major signing of the summer.