Israel reportedly is working on a plan to offer monetary compensation to relatives of nine Turkish activists killed in May during a raid on a ship attempting to break an economic blockade on the Gaza Strip.
Turkish media reported Thursday that Israeli officials are working on their response with Israeli officials.
However, the Reuters news agency quotes an unnamed Israeli official as saying any diplomatic move to appease Turkey will be tied to Ankara's help in indemnifying the Israeli navy against lawsuits.
Turkish Prime Minister Recept Tayyip Erdogan had asked Israel for an apology and compensation.
Since last month's events, diplomatic relations have been frosty between the two countries. But Israel's deadly forest fires have provided a recent thaw.
Earlier this week, the Turkish government sent fire-fighting planes to help Israel contain the blaze.
In response, Israeli Prime Minister Benjamin Netanyahu called his Turkish counterpart to thank him. It was the first conversation between the two leaders since the death of the Turkish activists.
Up to that point, Turkey and Israel had enjoyed close political and military relations, including Turkey playing a key role as a mediator in peace talks between Israel and the Palestinians.