The England midfielder was on the point of being transferred two weeks ago when Newcastle upped the price by £2million, saying they had initially under-valued the player.
West Ham had agreed a fee of £5million up front for the 28-year-old with a further £1million depending on appearances and refused to increase their offer.
It is understood that fresh talks have taken place within the last 24 hours and that both clubs are keen to revive the deal, possibly with West Ham offering to pay the whole £6million up front for the attacking midfielder.
Newcastle are still hoping they can get closer to their 'revaluation' of £8million.
Dyer has wanted to move back to his home town of Ipswich, which is 45 minutes from West Ham's training ground, and Newcastle had made it clear to the attacking midfielder that he was surplus to manager Sam Allardyce's requirements.
West Ham are treating the latest round of talks with caution however after feeling they had agreed a deal last time only for Newcastle to move the goalposts.
The fee for Dyer will free up some spending money for Allardyce, who has been linked today with a move for one of his former players at Bolton, Senegalese central defender Abdoulaye Faye.