Khune was thought to be among the highest paid players in the League before his contract at Kaizer Chiefs ran out last month. His reported high demands could prove to be out of reach even for the big-spending Chloorkop side.
Sundowns coach Pitso Mosimane did not mince his words when asked if they are chasing the clubless keeper.
"I believe Khune is the number one keeper in the country. It's not easy to sign a player. If you want to sign a player, you must also afford him," says the outspoken coach.
"I'm not saying we can't afford him but it must be market related. Look at Elias Pelembe, he had to leave and take a pay cut at Bidvest Wits. I wish he could have taken the pay cut here.
"It's tough and this is to show that people must play for their money and it must be market related and South African players must understand that now. People are being given clearances at big teams and going to smaller teams for less money."
Mosimane adds: "There's competition now, the young ones are pushing and if you don't play for your money, you find yourself with a big name but not having a team and you go to other teams and they can't afford you.
"It's a problem and our players must realise that there's no money in Europe and South Africa is affected now, so they must earn their money and enjoy it while they are still earning much."
The Brazilians claimed the Etv Charity Showdown title on Sunday, a pre-season tournament played at the Lucas Moripe Stadium, with a dominant 3-1 win over Ajax Cape Town.