Ties between the two countries hit an all-time low following the deaths of nine Turkish activists killed by Israeli commandos who boarded the Mavi Marmara as it attempted to break the Gaza blockade in May 2010.
Ankara has repeatedly asked Jerusalem to issue a formal apology and compensate the victims' families. Israel insisted the soldiers acted in self-defense. Turkey then expelled Israel's ambassador and cut all military ties with Jerusalem.
The latest request was raised by Pinhas Avivi, the former Israeli ambassador to Turkey who serves as the political director of the Israeli Foreign Ministry, the Turkish dailies Hurriyet Daily News and Today's Zaman said, during a Jerusalem meeting Monday with Turkish journalists.
Avivi suggested the two countries should hold talks on the situation in Syria, saying both countries will be affected by the outcome.
"Israeli officials should take the steps expected [by Turkey] to normalize relations instead of giving messages through statements to press," Hurriyet quoted Selcuk Unal, a spokesperson for the Turkish Foreign Ministry, as saying Monday.
"We should leave aside the problems between Israel and Turkey and look to the future," Avivi countered.