The club announced on Twitter that they have opened negotiations with the 32-year-old, who is available on a free transfer following his release from Manchester United
Owen is available on a free transfer having been released by Manchester United this summer, and has previously hinted he would listen to offers from club sides around the world, having spent time abroad earlier in his career with current Spanish champions Real Madrid.
Al Shabab has now claimed that a meeting with the 32-year-old's representatives is due to take place, and that negotiations to bring the England international to the club could be concluded 'soon'.
They announced via Twitter: "Michael Owen has been identified as a candidate to play for Shabab next season and we are in negotiations with his management team.
"The player's agent is in Dubai to close the deal."
A spokesman for the club, who are set to compete in next season's AFC Champions League, added: "We are in talks with the player and his agent, but no agreement has yet been reached between the parties.
"Things should become clear soon."
Stoke City had previously been linked with the former Liverpool man, with boss Tony Pulis admitting he would be interested in signing the player having missed out on his signature three years ago.
Owen was signed by Sir Alex Ferguon in 2009 after he left Newcastle, but he has struggled to make an impact at Old Trafford after fitness problems limited him to just 31 appearances in three years.
He was released at the end of the season, having made just three appearances in the whole of the campaign, but he has since insisted he feels capable of playing at a high level for a few more years.