Al-Ettifaq have been negotiating with the player’s entourage but have not received the green light to approach the club.
However, there is an expectation that the Hammers will let him leave if they receive a good offer.
Antonio has been a loyal servant to West Ham United. He joined them from Nottingham Forest in 2015 and has become an integral part of the squad.
The 33-year-old has played 276 games for the London club, bagging 75 goals and 43 assists.
He started as a full-back but moved to the centre-forward position, where his hold-up and linkup play has been crucial for his side.
West Ham may consider selling Antonio and refreshing their forward line. They have Danny Ings and Gianluca Scamacca on their books, but they have not lived up to expectations.
Scamacca was particularly disappointing as he came with plenty of promise and a hefty price tag but only bagged eight goals in 27 appearances for West Ham. He has been angling for a return to Serie A.
Ings has only scored three goals in 27 outings since joining the club. He has not kicked on and may leave this summer too.
West Ham must consider whether to dip into the transfer market for new striking options ahead of next season.
They have been focused on midfield reinforcements following the departure of Declan Rice to Arsenal. They are eyeing moves for Edson Alvarez, Denis Zakaria and Joao Palhinha.
Fulham knocked back their £45 million offer for the latter, but they will likely make another bid.
West Ham are the top candidates to sign Southampton midfielder James Ward-Prowse.