Upton Park owners David Gold and David Sullivan should announce the deal within a week.
They previously promised the Hammers faithful they would not sell the midfielder, 29, to Spurs.
A source revealed to The Sun: "Parker will become a Hammer for life if the owners have their way.
"He is earning top money at this club - well over the £60,000 which represents the Tottenham wage ceiling.
"He has never given any indication he wanted to go anywhere."