Barton looks set to leave Manchester City after being suspended by the club following his training ground bust-up with team-mate Ousmane Dabo.
Newcastle are believed to be in the driving seat for Barton as Sam Allardyce looks to make the midfield firebrand his first signing at St James' Park.
However, West Ham are now hoping to scupper Newcastle's bid to sign Barton by offering him the option of a move to Upton Park instead.
Both clubs are ready to activate the buy-out clause of £5.5million in Barton's City contract to hold talks with the England international.
Barton's potential move to either club all depends on Scott Parker's proposed move from Newcastle to West Ham.
Barton's agent Willie McKay admitted West Ham were monitoring the player's situation and that the midfielder is waiting to see what offers come in for him.
"I believe West Ham are interested in Joey as well as Newcastle, but everything depends on the possible transfer of Scott Parker," McKay told skysports.com
"If the clubs make an offer of £5.5million they can activate Joey's clause in his contract.
"We are now waiting on offers to come in before we take things further."