The Slovenian government has also discussed the matter but has made no final decision yet, Delo said.
Tuerk would not comment on reports that he wants to run for the office which incumbent UN Secretary-General Ban Ki-moon will leave in 2016.
Also being considered is the option of giving Tuerk special status so that he can lobby international politicians, Delo said, recalling that his status as former president, which entitled him to a salary, administrative staff and his own office, expired this year. A decision to abolish former presidents' offices has been adopted to slash and stabilise costs.
Delo also reported that former Slovenian Prime Minister Alojz Peterle, whose term as a member of the European Parliament expires next year, wants to run for Council of Europe secretary-general. According to unofficial information, Foreign Minister Karl Erjavec is against it.