The Blues are in the market to improve their squad following a disappointing fifth-placed finish in the Premier League table.
Chelsea FC are facing the prospect of losing Belgium international Eden Hazard to La Liga giants Real Madrid this summer.
Lemar was close to a move to Arsenal last summer but the France star turned down a move to the Gunners after AS Monaco agreed a £92m fee.
The attacking midfielder was also linked with Liverpool FC but Lemar ultimately remained at AS Monaco for another season.
Lemar scored two goals and made eight assists in 33 appearances in the Ligue 1 season to help AS Monaco secure second spot in the table.
Atletico Madrid are also being linked with a move to sign the 22-year-old forward with uncertainty surrounding Antoine Griezmann’s future.
Sky Sports News reporter Solhekol believes Chelsea FC and Tottenham Hotspur are interested in a move to sign Lemar.
“Chelsea are interested in him,” Solhekol told the Transfer Talk podcast. “Spurs are interested in him. Atletico are the favourites to get him.”
Chelsea FC were 1-0 winners against Manchester United in the FA Cup final at Wembley after Eden Hazard’s winner from the spot.
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