The France international has become a key target for new manager Xabi Alonso as the Blues look to strengthen their defence.
According to The Times, the Eagles value the 26-year-old highly after his impressive performances since joining from Wolfsburg two years ago.
With three years remaining on his contract, the Eagles are in a strong position and believe Lacroix should command a fee similar to recent big-money centre-back transfers.
Chelsea are also planning defensive changes, with Axel Disasi and Trevoh Chalobah potentially leaving Stamford Bridge.
The Blues have already added Marco Palestra from Atalanta but remain keen to reinforce their backline.
Palace are preparing for a possible departure by exploring defensive options, including Oscar Mingueza and Chrislain Matsima.