The News of the World says the Australian international has settled in quickly to his new surroundings in London and was handed the captain's armband by Alan Curbishley at the start of last season.
The former Blackburn defender is reported to be earning £60,000 a week and there has been speculation that the club are looking to reduce their wage bill.
But Neill's agent Paddy Dominguez recently dismissed reports that he would leave West Ham during the summer and is happy to remain at Upton Park.
Dominguez said: "It doesn't make sense that a manager who 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."