It has been a disappointing debut campaign for the £44m signing from Porto.
The Brazilian centre-back has made just 13 appearances all season.
And Don Balon says the Gunners are hoping Real will entertain an offer for his signature.
Mikel Arteta is desperate to bolster his defence over the summer and he has been impressed by 22-year-old Militao.
Manchester City and Tottenham Hotspur are also interested in the Brazil international.