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"Mathoho is still number one on our wish list," said Amakhosi general manager Bobby Motaung.
He said Chiefs had approached Celtic directly with the offer.
"Whether it is this week, next month or even next year, we want the player to come to Chiefs. I hope Celtic will come back with a positive response. His jersey is waiting for him in Naturena," said Motaung.
Sowetan has learnt that free-spending Mamelodi Sundowns are also after Mathoho's signature.
The lanky Bafana defender is reported to have told Celtic bosses to forget about taking him to Chloorkop, saying he wanted to go to Naturena where he believes he will get regular game time.
Celtic chief executive Khumbulani Konco said: "At the moment Mathoho is still our player, we will release him as soon as we find a replacement."
Amakhosi are also courting Leopards' trusty striker Kingston Nkatha but club boss David Thidiela says the Zimbabwean is not for sale.
Thidiela confirmed that Chiefs had wanted to buy Nkatha, but the approach had been rejected. "There is no way I will sell any player," said Thidiela. "(Instead) I'm beefing up the team so we do well in the CAF Confederation Cup."
Leopards are due to meet El Merreikh of Sudan next month in the continental tournament. Thidiela contradicted Leopards spokesman Tendani Thidiela, who said the club would seek a player and cash in return for Nkatha. He suggested that such a player could be Chiefs centre-back Thomas Sweswe.
"We would not look at a straight swap because Kingston holds a higher value than Sweswe, but Thomas would be a good addition to our squad and if he were to form part of a deal that sees Kingston go to Chiefs then we would welcome that," said Thidiela jnr.
Nkatha, 26, had a fine end to the 2011-12 PSL season, his goals in both the league and the CAF Confederation Cup helping Leopards to top-flight survival and the playoff rounds of the African club competition.