But the Hammers' offer is thought to be considerably less than the £8.5million which has been reported.
West Ham manager Alan Curbishley is in the market for a central midfielder with captain Nigel Reo-Coker set to leave Upton Park this summer after handing in a transfer request.
Parker, 26, is thought to be keen on a move back to London and a switch to West Ham would see him link up again with Curbishley, his old boss at Charlton.
Parker spent seven years with Curbishley at The Valley and made his England debut against Denmark in 2003 before completing a £10million move to Chelsea.
With first team opportunities limited at Stamford Bridge, Parker moved to St James' Park in 2005 and was made Newcastle captain last summer.
New manager Sam Allardyce has been linked with out-of-favour Manchester City midfielder Joey Barton as a potential replacement for Parker.
Vi bruger cookies for at kunne give dig den bedste oplevelse. Ved at bruge vores side accepterer du brugen af cookies. Du kan læse mere i vores persondatapolitik.