Arsenal and Tottenham have both been linked with a move for the 30-year-old England international.
But new West Ham boss Sam Allardyce will make one final effort to convince Parker to lead the club back into the Premier League.
"That will be an issue for Sam. He will be back in the office on Monday and I guess that's when the hard work starts."
If Parker does move on, Allardyce has a ready-made replacement in midfield in the shape of Kevin Nolan.