West Ham are also interested in Paulo Fonseca, manager of Ukrainian club Shakhtar Donetsk.
West Ham confirmed Moyes's exit on Wednesday and Sullivan thanked him for his efforts after becoming a member of in November - once they sat within the drop zone.
The ex-Manchester City manager has been in charge of Hebei China Fortune since 2016 but could be set for a Premier League return after being installed at 8/11 (1.73) by Paddy Power.
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'Throughout his time here, David has carried himself with dignity and honesty and we have all found him to be a pleasure to work with, ' said Sullivan.
West Ham's backroom employees of Alan Irvine, Billy McKinlay and Stuart Pearce have additionally left the membership and the Hammers wish to title a "high-calibre determine" inside the subsequent 10 days.
The Spaniard nearly became Hammers boss in the summer of 2015, but they were ultimately beaten by European giants Real Madrid - although the West Ham owners Gold and Sullivan are thought to still be on good terms with Benitez. "They deserve great respect for the job they have done and they leave the Club with our best wishes", Sullivan added.
According to a club statement on Wednesday, Moyes only came to the London club with the sole objective of ensuring the Hammers' Premier League status - which he has achieved.
Former Man City boss Manuel Pellegrini is now top of the betting (see more details below), he is managing in China at the moment.