The Brazilian has been heavily linked with a move away from the Santiago Bernabeu after falling down the pecking order under Jose Mourinho.
"Kaka could join us, yes, but at this time I cannot guarantee it," said Unal Aysal.
"If we negotiate the group stage of the Champions League we will try to get hold of him.
"I think that he would integrate well in our club and we would love to see him wearing the shirt of Galatasaray."
Kaka joined Madrid from AC Milan in 2009 for around £35m.