There is "a lack of commitment" from both sides with regards to Moyes staying at West Ham, and Shakhtar Donetsk manager Fonseca is one of two managers mentioned as attracting West Ham's interest.
But when questioned on whether or not he could now categorically state if he wants the West Ham job, Moyes said: "I can't because I'm no further forward".
"I'm really happy with the last six months and we will see what happens".
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The Scot, appointed in November as successor to Slaven Bilic, steered West Ham to Premier League safety in a campaign capped by two goals from Manuel Lanzini and Marko Arnautovic's 11th of the league season rendered Oumar Niasse's strike a consolation.
Speaking to Monday's Alan Brazil Sports Breakfast, Ashton said: "I think the fact we've not heard anything yet makes me think he will definitely leave and they'll bring somebody new in". "When you have good performances you might see there is something to build on".
But the former Manchester United manager has experienced difficulty getting to grips with the club. "I'll take my suit off at midnight okay, undo my tie a little bit...be back on the streets come midnight!"
Moyes' opposite number Sam Allardyce spent just three and a half minutes summarising his thoughts on the game to reporters, and rebuffed questions about Wayne Rooney's future amid rumours the former England striker is set to join DC United in MLS.