Saudi top flight outfit Al Ettifaq are currently managed by Liverpool legend Steven Gerrard and are in the process of bringing in Reds skipper Jordan Henderson.
The club are expected to back Gerrard with more signings and Antonio is of interest.
There have been talks with the player’s camp, but they are still at an early stage and West Ham have not been approached.
However, it is suggested that West Ham will let Antonio go if an acceptable offer arrives.
A lucrative offer from Saudi Arabia could be too good to turn down for Antonio this summer.
West Ham are expected to revamp their attacking options over the course of the transfer window and Gianluca Scamacca could return to Italy.
Scamacca struggled to make an impact in the Premier League last season as West Ham fought against relegation and he is wanted by several Serie A sides.