The 34-year-old joined the Foxes on a shock one-year deal last summer upon their promotion to the top tier and played a key role as the club put together a fantastic late run of form to avoid the drop.
New King Power Stadium chief Claudio Ranieri – who coached the veteran at Inter Milan – attempted to persuade the five-goal star to stay, but Cambiasso has left in search of a fresh challenge.
And reports claim that the Hammers are eager to offer him just that at Upton Park.
Slaven Bilic’s side are facing an arduous campaign in which they will have to balance Europa League football and domestic responsibilities, so fresh faces are key for the Croatian as he sets about bulking out his squad.
Although at his age Cambiasso could be tempted by a money-spinning move to the likes of Major League Soccer or the Middle East, the prospect of continental football in East London may appeal to him.