Parker returned to the Championship club for pre-season training and was set to meet his new manager for the first time.
Allardyce previously said that he wanted to talk to all his international stars face-to-face rather than over the phone to discuss their futures.
Crunch talks: Scott Parker set to discuss his future with new West Ham manager Sam Allardyce
It has been expected that Parker would leave the east London club following last season's relegation, with Harry Redknapp and Spurs interested in signing the 30-year-old.
So far only Turkish giants Fenerbahce are understood to have tabled a bid, but Parker is understood to be reluctant to move abroad.
Up in the air: Goalkeeper Robert Green is another West Ham player due to discuss his future
Fellow England stars, Robert Green and Carlton Cole, are also due to discuss their situation with the new Hammers boss as well as highly rated youngsters James Tomkins and Jack Collison.
The Hammers travel to Switzerland at the weekend for a pre-season tour and Allardyce will decide which players to take with him and who to leave behind to sort out their futures.
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