The 32-year-old is out of favour at Stamford Bridge and out of contract next summer leaving West Ham to eye a January move for the centre-back.
Pellegrini’s adventures in the transfer market have so far been backed by the Hammers board as the squad bounces back from their dreadful start to the season. Unbeaten in three of the last four in the Premier League, the Chilean is keen to add depth to his defence, as well as experience to nurture the footballing growth of Declan Rice, 19.
The defeat at Brighton last time out underlines that there is still much work to do if there is to be a serious improvement from last season.
Cahill’s career prospered under Antonio Conte as the Italian sought to right a listing ship as Chelsea surrendered their league title to Manchester City. Cahill captained the FA Cup winning side at Wembley last season, depriving former boss Jose Mourinho of silverware in his second season in charge at Old Trafford.
The arrival of Maurizio Sarri however, saw his career tank. One Premier League appearance and two cup games is a signal that his future lies elsewhere.