The pair were part of the side that dumped Manchester City out of the UEFA Champions League, and Conte is prepared to offer a substantial fee to tempt the Ligue 1 club to sell in the summer.
Steve Stammers of the Mirror reported the Premier League leaders will put £40 million on the table, and Conte is said to have "been hugely impressed with the performances of the 22-year-olds."
According to Stammers, Mendy is currently valued at £12 million and would be purchased to strengthen the Blues' left-back position. Portugal international Silva would cost £28 million and can play in a number of attacking roles.
Here is Silva in action:
Mendy can also feature as a defensive midfielder but has greatly improved at left-back during his side's excellent run in Europe.
The player has eight assists in Ligue 1 and the Champions League this term in 25 appearances, according to WhoScored.com, and he would provide Conte a productive outlet.
However, football writer Andrew Gibney believes Mendy's final ball can often let him down:
According to ESPN FC, Manchester City also want a new left-back and will target Mendy, with manager Pep Guardiola making the position a priority if he looks to replace Gael Clichy. The France international was caught out as he conceded a penalty against Liverpool at the Etihad Stadium on Sunday, with the Sky Blues' defensive issues still evident.
Conte has produced wonders to put Chelsea in the title picture this season, but their squad is still thin compared to their top-four competitors in the Premier League.
Mendy and Silva would be perfect additions, and at £40 million—they would not be overpriced.
Victor Moses has been a fantastic auxiliary right wing-back this season, but there are a number of roles Conte could quickly improve with shrewd buys.
Marcos Alonso has been a revelation since signing from Fiorentina, and his form might prevent his manager from adding a top-class left-back when there are clearer needs in other parts of the pitch.