The Sun says talks between West Ham and Spurs have collapsed after a wrangle over the £6million deal.
Hammers boss Sam Allardyce hoped to get promising midfielder Jake Livermore, 21, on loan for the season as a makeweight.
But Spurs have backtracked because of the uncertainty surrounding Luka Modric's future.
A deal for Parker, 30, looked done on Sunday and the England midfielder was left out of the side that won at Nottingham Forest.
Parker wants to leave but West Ham are digging in with just 36 hours left until the transfer window shuts.