With the Blues still in the hunt for a new frontman after deeming Diego Costa to be surplus to requirements, their attention is reported to have drifted towards a London rival.
Belgium international Benteke is among those said to be on their radar, with Antonio Conte having already seen Romelu Lukaku snub a potential return to Stamford Bridge in favour of making a £75 million move to Manchester United.
Various other options have been linked with the reigning Premier League champions, such as Alvaro Morata and Andrea Belotti, and Palace have warned anyone considering an approach for their star striker that they have no intention of sanctioning a sale.
New Eagles boss De Boer told reporters when quizzed on the exit rumours: "He's happy here and we really want him to stay.
“He made a great impact last season, especially in the second half of the season, and he is crucial to us and we don't want to sell him."
Palace signed Benteke from Liverpool in the summer of 2016 for £27 million, having seen him struggle to make an impact during a solitary season at Anfield.
The 26-year-old netted 17 times for the Eagles in all competitions during his debut campaign, with 15 of those efforts coming in the Premier League – his best return in the English top-flight since his first year with Aston Villa in 2012-13.
His physical attributes would make him a logical choice to replace Costa at Chelsea, but Conte may have to look elsewhere as he seeks to fill an important gap in his squad before the summer transfer window closes.