The attacking midfielder, who is one of Chiefs' huge fan-favourites, had a poor 2016/17 season which saw him fail to replicate his old form.
However, according to the latest reports the Mamelodi giants are still keen to land his services from Amakhosi ahead of the 2017/18 campaign which will start next weekend.
Lebese, who missed the recent 2017 Carling Black Label Champion Cup clash with Orlando Pirates, is said to have told Chiefs his desire to leave and he still has a year left on his current Amakhosi deal.
Sundowns head coach Pitso Mosimane, who is known to be a big fan of Lebese, is reportedly pushing the Brazilians management to sign the 28-year-old winger.
Negotiations are believed to be on-going between Chiefs and Sundowns, who recently reportedly failed to sign Cape Town City winger Aubrey Ngoma as their bid was rejected by the Citizens.
The Brazilians are expected to sign a quality left winger during the current Transfer Window as a replacement for Keagan Dolly.
The Bafana Bafana international left Sundowns for French side Montpellier HSC midway through last season.