The 26-year-old will enter the final six months of his contract with Phunya Sele Sele next week, and he has already informed the Free State outfit that he won't be renewing his contract with them.
According to a source close to the player, Amakhosi have already held talks with Celtic over the possibility of having Mahlasela when the January transfer window officially opens on January 2.
However, Celtic are prepared to lose their star player for free should any of his suitors fail to meet the club's asking price.
"The latest news is that Celtic told Chiefs to meet their asking price or wait until July to have Mahlasela," the source told Goal.
"The two clubs have already held talks, but no agreement was reached. The ball is firmly in Chiefs' court. If they don't want to pay for the player, then they will have to wait until he's a free agent," added the source.
Mahlasela is also wanted by Orlando Pirates, and chances are that he could return to Parktown should the Soweto giants be willing to strike a deal with Celtic.
The speedy attacker has managed 14 appearances in all official matches under Veselin Jelusic so far this season.