The 66-year-old Hollander's deal expires at the end of the season and Ajax have offered him a new one-year contract, but the coach says he still has to consult his family before taking a decision.
He tells East London's Daily Dispatch that his wife, who lives in Holland, won't be happy with the idea of her husband being away in South Africa yet again.
"You might remember that we offered the coach a contract until the end of the season and we even told him that we would give him another deal if he is happy with working and staying in Cape Town," Ajax spokesperson Shooz Mekuto said.
"He has indicated to us that he loves coaching our team and he also loves the city, but the problem is that he still has to consult with his wife before taking any decision. It might happen that his wife might says no to him remaining as our coach.
Ajax CEO George Comitis confirmed Mekuto's comments. "The matter is still very much in the discussion phase and nothing has been decided at this stage. We would like to extend the coach's contract for another year, but at the moment he needs time to check on his personal issues, including that of his wife being based in Holland."
De Haan arrived at Ajax to succeed Muhsin Ertugral, who left the team to coach Turkish side, Sivasspor last October.