The Daily Mail report that Fonseca travelled to the home of West Ham co-owner David Sullivan for a 75-minute discussion on Monday evening.
The leading candidates to follow Moyes in the West Ham hotseat are as follows.
I also understand that Sullivan already knows who he wants and Benitez, a man who he has nearly landed before, is his preferred candidate.More news: Brent crude hits new 3½-year high as sanctions' impact unclear
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"I have another year of my contract and we are trying to do our best to do what we have to do to go forward". We will meet and talk I think this week.
"They made me some offers to stay here for a few more years, plus I have to manage my family: if I chose to go to Newcastle and stay there, even in the Championship, it's also because of my family".
Has Newcastle manager Rafa Benitez given hope to Everton and West Ham of signing him?
However with West Ham looking at their options the Scot could decide to walk away and seek employment elsewhere. Burnley's Sean Dyche and Fulham chief Slavisa Jokanovic are also high on Sullivan's shortlist, whist some big foreign names like Manuel Pellegrini and Daniel Fonseca have also been linked.