Tottenham apparently inquired about the 24-year-old first, though Chelsea have sped past their London rival with a formal offer for Lemar.
Both sides have been linked with a slew of attacking players during the winter transfer period and are both reportedly eager to sign Lemar on a short-term basis before evaluating if the World Cup winner merits a permanent deal.
Chelsea have monitored Lemar for some time, according to Burt, and Liverpool and Arsenal expressed an interest in the Caen academy product before he joined Atletico.
The Blues are also reportedly keen on Borussia Dortmund whiz Jadon Sancho and Lyon striker Moussa Dembele, while Spurs are pursuing attacking options in light of Harry Kane's latest long-term spell on the sidelines with a torn hamstring.
Lemar has not impressed since making a €60-million move to the Spanish capital from Monaco in 2018, and Atletico boss Diego Simeone has confirmed as much, saying that Lemar failed to "live up to expectations." He has scored just three goals in 47 La Liga outings over a season-and-a-half in Spain.