Mweene would replace Hans Vonk, who has retired.
The Zambian international had been in talks with Ea Lla Koto about renewing his contract, which comes to an end next month, but now looks set to leave the team.
Ajax CEO George Comitis reveals to KickOff.com that Mweene is on their list.
“We are interested in him but we have not spoken to him directly; he is a very good keeper and we would love to have him here,” he says.
Speaking to KickOff.com from Zambia, where he is on national team duty, Mweene confirms that negotiations between him and Free State Stars have stalled.
“I have not signed a new deal with the club but we are still negotiating so we will wait to see what happens,” he says.
“The delays are from my side and not the team but at the moment I’m with the Zambian national team and I cannot comment further than this."
However, Stars chairman Mike Mokeona says Mweene is not going anywhere.
“He is not for sale and whoever told you that they are interested tell them he is not for sale ... Mweene has a lifetime contract with us and he is not going anywhere,” he said, before hanging up his cellphone.
Mweene, who joined Stars from Zambia's Kitwe United, has had a successful stint in South Africa and was the club's 2008/09 Player of the Season.