West Ham co-owner David Sullivan has offered the 32-year-old a two-year deal, worth more than £7.5million, according to The Sun.
The Hammers are ready to pay Henry around £75,000-a-week.
Sullivan told The Sun: “We’re trying to assemble a more prolific strike force at West Ham and I’d love to have Henry here.
“Our club is in debt but a striker of his quality and standing would make it a great deal. Henry is still up there with the best.
“I’ve made an offer which would make him the highest-paid player in the club’s history.
“And it’s a serious offer because Henry could walk into almost any Premier League side.”
