Benteke seems like the most likely candidate to arrive at West Ham, due to his struggles at Liverpool.
The powerful Belgian has been linked with the Hammers throughout the season, and it is believed that they have kept a close eye on the former Aston Villa man.
Benteke has scored just eight times in the Premier League this term at Liverpool, but he has proven before that he can be prolific in England.
The Manchester City forward is another player who has struggled since getting his big move.
Bony switched from Swansea City to the Etihad Stadium last year, but he has failed to make much of an impact with the Citizens.
Bony has started just 15 times in the Premier League, during an 18 month stay with City and he looks likely to move on this summer.
West Ham have been talking about their ambition for quite some time, and they have also stated a desire to bring in a 20 goal a season man.
The signing of Vardy would certainly outline their desire to start competing for the top four spots in the Premier League.
Vardy has blasted in goals on a frequent basis for the Foxes this term, and persuading him to leave would be difficult, but even submitting a bid for the former Fleetwood man would show the sort of market that West Ham are now shopping in.
West Ham are also said by The Sun to be aiming to sign to Arsenal's Theo Walcott, as they look to strengthen their forward line.