However, the Australia defender's manager Paddy Dominguez dismissed the report and insists neither he nor Neill had had contact with the club over the matter.
Dominguez told Fox Sports: "We have not been approached by West Ham in regards to that, reviewing his contract or taking a pay cut.
"It doesn't make sense that a manager who only 14 months ago brought Lucas to the club and has installed him as captain would look to sell him.
"It would be very strange. Lucas' relationship with Alan is good and he is relishing the role of captain.
"Seeing that it's come from the British tabloids and no quote from Curbishley or West Ham, I wouldn't give it too much credibility."