The 21-year-old has long been linked with a move to Ajax and Heerenveen have granted the club permission to open talks with Narsingh.
“Ajax have already made an official offer, but that has been turned down,” Hansma said to De Telegraaf.
“We are eager to hold on to Luciano, but we know that he wants to move. We have now told his agent to see whether they can agree personal terms.
“If he doesn’t sign a new deal with us, we will try to sell him in order to prevent him from leaving on a free transfer next year. However, if nobody meets our demands, we will be more than happy to keep him for another season.”