ATHENS, May 14 (Reuters) - Greece aims to tap bond markets next year, Prime Minister Alexis Tsipras told a Greek newspaper after debt relief talks started between Athens and its lenders at the start of this week.

"We will return to the markets in 2017," Tsipras said in an interview with weekly Realnews newspaper, according to the paper's website.

Cut off from debt markets since 2014, Greece signed up a third international bailout last summer and hopes to conclude a bailout reform review with its EU/IMF lenders on May 24 to unlock fresh fund it needs to pay EU/IMF bonds and state bills.

"We might exit the bailout once and for all a lot before the programme expires in August 2018," Tsipras said.

(Reporting by Angeliki Koutantou; Editing by Janet Lawrence)