Sky Sports says Chelsea higher-ups, including former Nigeria international Michael Emenalo who is the technical director, have been impressed with Moses in his new right wing-back role, and are looking to tie him down to a new long-term deal.
The Super Eagles star has three more years left on his current deal, having penned a contract extension before joining West Ham on loan last season.
Moses has scored 3 goals in 12 Premier League appearances this term, behind only Hazard and Diego Costa.