But sources close to the Irons board have immediately ruled out the Uruguayan as a possible to take over from under threat Sam Allardyce.
The Sunderland boss was at the centre of speculation a few weeks ago that he would be ready to leave Sunderland at the end of the season.
At the time the Black Cats looked dead and buried as a Premier League force but have sensationally recovered to nail their spot in the big league with four straight wins against Chelsea and Manchester United (away) and Cardiff City and West Brom (home) have kept them afloat.
Poyet was eventually forced to deny the stories of his possible departure from the club but his emergence as a 6/5 favourite caused immediate excitement around the Boleyn.
However, a source close to the Hammers powerbrokers told ClaretandHugh exclusively: ” Gus’s name has been mentioned along with Malky Mackay and Harry Redknapp but he was immdiately ruled out on the basis of Premier League inexperience.
“Malky is also in much the same position whilst you can forget Harry – he won’t be returning.”