Lemar had been linked with a move away from the Spanish capital after another underwhelming campaign with Los Rojiblancos.
According to reports from the Daily Express, the English pair were contacted over a move for the 26-year-old, but neither expressed an interest.
That prompted Lemar to accepted his restructured deal with Atletico but his long term future is uncertain under Diego Simeone.
Arsenal famously tried to sign Lemar from AS Monaco, just days before he joined Atletico in 2018, with former boss Arsene Wenger rumoured to have made a last minute £92m bid.
The Gunners have already laid out £120m on new players this summer, including Gabriel Jesus, Oleksandr Zinchenko and Fabio Vieira, with Everton yet to spend a penny in the window.