The Mail suggest that Crystal Palace and Aston Villa are also interested in signing the former Queens Park Rangers striker.
Remy has found first team chances hard to come by at Chelsea this season, with Diego Costa and Eden Hazard seemingly ahead of him in the pecking order.
Although a permanent deal for Remy seems unlikely, both West Ham and Southampton are optimistic over the potential for a loan switch.
Slaven Bilic’s side have already done business with Chelsea this season, having taken Victor Moses on a season-long loan from the near neighbours.
Southampton, meanwhile, would be able to offer Remy regular first team action, with Graziano Pelle and Shane Long likely to be his main competition up front, if he was to move to St. Mary’s.