The Hammers chief executive, Scott Duxbury, is understood to have held talks with Parker's representatives late on Wednesday night, following the late intervention from Tottenham.
And Londoner Parker is believed to be meeting West Ham officials today (Thursday) after the two clubs agreed a fee for the defensive midfielder.
England international Parker, 26, played for West Ham manager Alan Curbishley when they were both at Charlton Athletic.
Curbishley was a reluctant seller of his skipper when Chelsea made a big-money move for the player during the 2003-04 season.
But Parker failed to command a regular starting place at Stamford Bridge and was transferred to Newcastle in 2005 for £6.5 million after making just 15 Premiership starts in a season-and-a-half at Chelsea.
Ex-Newcastle boss Glenn Roeder made Parker captain of the Magpies a year ago.
But he is unsettled in the north-east, and now the Hammers are seeking a new central midfielder, as captain Nigel Reo-Coker looks certain to leave Upton Park this summer.
Parker and Curbishley were together for seven years at The Valley. He made 128 League appearances for Charlton and also made his England debut while with the Addicks (against Denmark in 2003).
He moved to Chelsea for £10m during the January 2004 transfer window..
If Parker gets his desired move back to London, Newcastle manager Sam Allardyce could move for a replacement by lining up a bid for Manchester City's controversial midfielder Joey Barton, who is seriously out-of-favour at Eastlands.