The 22-year-old centre-back played 22 games for the Italian outfit last season and helped them to stave off relegation, finishing in 16th place in the table.
Following an impressive campaign with Spezia, the Polish international was the subject of interest from a number of clubs this summer.
David Moyes’s side were keen on bringing the player to London Stadium, but Kiwior decided to stay with Spezia for the time being.
It has been suggested that West Ham have retained their interest in the centre-back and might well go back to the Italian outfit in the winter transfer window for the player.
However, according to Italian outlet Calciomercato.it, Juventus are scouting Kiwior and might submit a bid in January to lure the player away from Spezia.
AC Milan are another club who are monitoring Kiwior’s situation and Paolo Maldini is an admirer of the player.
The Hammers have recruited Nayef Aguerd and Thilo Kehrer to strengthen their defence, and it remains to be seen whether Moyes’ side will add another centre-back in the January transfer window.