Cahill, 32, has made 285 appearances for Chelsea since a 2011 move from Bolton Wanderers.
Just three of those appearances have come during the 2018-19 campaign, however, and the experienced defender has made just one Premier League outing for the Blues this term.
Cahill's contract with Chelsea will expire at the end of this season, and it is thought that the Englishman could leave Stamford Bridge when the January transfer window opens for business.
According to The Mirror, West Ham boss Manuel Pellegrini is an admirer of Cahill, and is keen to bring the defender to the London Stadium at the start of 2019.
Cahill has won one Champions League, one FA Cup and two Premier League titles during his time at Chelsea.