It has been reported by the British tabloid that the former Argentina international midfielder is “wanted as part of new Hammers boss Slaven Bilic’s cultural revolution”.
The London outfit have already “made contact” with Cambiasso’s agent, according to the report.
It has also been claimed by The Sun that West Ham are ready to offer “top wages” to Cambiasso if they can get him on a free transfer.
Cambiasso joined Leicester on a one-year contract in the summer of 2014 after leaving Italian giants Inter Milan.
The former Real Madrid midfielder was one of the best and most influential players at Leicester and was a key figure in their survival battle in the recently concluded 2014-15 season.
The 34-year-old scored five goals and created 36 chances in 31 appearances in the Premier League.
Cambiasso had a pass accuracy of 73% and a shot accuracy of 32%, and won 36 headers, 14 dribbles and 43 tackles.