CAIRO, Sept 9 (Reuters) - Qatar agreed on Monday to convert a $2 billion deposit with Egypt's central bank into bonds within a week, Youm 7 newspaper quoted central bank governor Hisham Ramez as saying.

The conversion was thrown into doubt last week when a central bank official said talks were under way and that Egypt was prepared to repay the $2 billion within days if negotiations to convert the funds into bonds did not succeed.

Qatar sent Egypt $3 billion in May of which it converted $1 billion into three-year bonds.

The central bank governor was not immediately available to confirm the newspaper report.

Cairo's relations with Qatar deteriorated after the Egyptian army deposed President Mohamed Mursi on July 3. Qatar had been a firm backer of Mursi's Muslim Brotherhood and lent or gaveEgypt $7.5 billion during the year he was in power.

On July 1, Egypt converted the $1 billion into three-year bonds at 3.5 percent interest and in May it converted another $2.5 billion of Qatari loans into 18-month bonds at 4.25 percent interest. The bonds were listed on the Irish stock exchange.