The Gunners wanted a closer look at the winger but the UAE club are only prepared to entertain transfer offers, while Angers midfielder El Jadeyaoui has been handed a two-day trial
The UAE Pro-League club revealed that the Gunners had invited the 21-year-old to train with them ahead of a potential move.
But Al Ain chairman Sheikh Abdullah bin Mohammed feels Abdulrahman does not need to prove his qualities in unnecessary trial stints and says the club will only listen to serious offers.
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"Omar is above having to go on trial to prove his skills, as he has played high-quality league and international matches, which are the real test.
"Any club willing to recruit Omar can check his performance in all his games and then submit a serious offer to sign him.
"If there is one, we are ready to negotiate with the team and reach a compromise."
Abdulrahman caught the eye of a number of clubs while playing for his country at the 2012 Olympic Games and in the AFC Champions League with Al Ain.
Meanwhile, the Gunners have handed a two-day trial to Angers midfielder Alharbi El Jadeyaoui, who was withdrawn from the Ligue 2 side's weekend clash against Istres.
Angers general manager, Olivier Pickeu, has confirmed the move but insisted that the two clubs are not discussing a permanent move yet.
"For Alharbi, this is something else," Pickeu told Ouest-France. "We're not in a negotiation phase yet.
"Arsenal have watched him many times, with Morocco as well. We thought it would be nice for him to spend time in England. It is rewarding for him and it is rewarding for us."
El Jadeyaoui, who spent a week-long trial at Blackburn in 2009, is a left-sided midfielder and could be seen as a replacement for Gervinho, who has agreed an €8 million move to Roma.