Benteke has long been on the Hammers’ transfer radar, with his £32.5 million move from Aston Villa last summer set to end in disappointment.
Burt claims that Slaven Bilic’s side are lining up Benteke, Marseille’s Michy Batshuayi and Lyon’s Alexandre Lacazette in a series of moves, hoping to land one of them.
It is believed that whichever club accepts their bid first would take priority in proceedings.
Liverpool would look to recoup much of their outlay from last summer, while the striker’s wage demands could be an issue, but co-chairman David Sullivan hinted this week that West Ham would soon lodge a bid.
“We’ve put a bid in today for €30 million for a player, and other bids will be going in.
“We’re going to make a £20 million or £25 million bid for a player in England later this week.
“Whatever happens we intend to bring a top striker in.”
The striker has previously expressed a determination to fight for his place on Merseyside, but the club could well make their feelings known if the Hammers force their hand with a bid.