"The ballot has been postponed till tomorrow," Petro Symonenko said before a roundtable with President Viktor Yushchenko.
The president's press service neither denied nor confirmed the information.
Yushchenko took a significant step toward resolving the country's protracted political crisis early Thursday by backing his long-time rival and the parliamentary majority's choice for the prime minister's job.
"I decided to nominate Yanukovych as prime minister," Yushchenko said before submitting the nomination of the pro-Russian Party of Regions leader, whom he defeated in the re-run of the 2004 presidential election, to the Supreme Rada.
Yanukovych previously served as prime minister under President Leonid Kuchma in 2002-2004.
The anti-crisis coalition that was formed from three parliamentary factions - Party of Regions, Socialists and Communists - nominated Yanukovych for prime minister in July. Yushchenko had to back Yanukovych's nomination before midnight local time (9:00 p.m. GMT) Wednesday or decide to dissolve the Supreme Rada, a move which former premier Yulia Tymoshenko and current leader of the opposition had supported.
