The 26-year-old Belgian frontman is believed to be a subject of interest for The Blues, and is touted as a possible replacement for a supposedly unsettled Diego Costa.
The Spain international was heavily linked with a move to the money-rich Chinese Super League at the start of January, and Antonio Conte is concerned that he might run short in striking options should a move eventually materialise.
Benteke has scored eight goals in 19 Premier Legaue appearances so far this season, since arriving at Selhurst Park from Liverpool in August last year.