The Gunners have made an offer for the United Arab Emirates international and want him to come across to England on a week's trial before they seal a move.
Barcelona and Schalke have also made their interest known but manager Arsene Wenger is hopeful that his side can tie up a deal quickly before either club can make the 21-year-old an offer, reports The Mirror.
Rashid bin Mubarak Al Hajri, deputy chairman of Al Ain, said: "Have we had an offer from Arsenal for him to come to train? Then yes.
"We have also had offers from Spanish teams and other teams, but the player will decide ultimately. We got a lot of offers for Omar. If he finds the right environment, then we will be very supportive.
"It's a package that will have to be right, where he can improve his football. I'll leave that for Omar - that's for him to decide."