The 28-year-old has been unsettled at the club over the last two seasons, and with his contract coming to an end in June 2018, Amakhosi could be tempted to sell him to the Tshwane giants.
Football manager Bobby Motaung confirmed that they have received an offer from the Brazilians, but he warned that they not reached an agreement on a transfer fee.
“We have received an offer from Sundowns. However, at this stage of proceedings an agreement regarding a transfer fee has not been reached,” Motaung told the Amakhosi website.
There have reports of a possible swap deal involving Mzikayise Mashaba going in the opposite direction, but neither side has been able to confirm the rumours.
Lebese sparked transfer speculation over his future when he took to social media to reveal that all he wanted was to play regular football.
This was after he spent last season playing second fiddle to Edmore Chirambadare during the second half of last season.