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In January, President Petro Poroshenko nominated acting central bank chief Yakiv Smoliy to be governor on a permanent basis, ending months of uncertainty over the highly-politicised position.
But the choice still has to be approved by parliament and Parubiy said the vote could take place next week.
"This issue is preliminarily planned for Thursday (March 1)," news agency Interfax Ukraine quoted him as saying.
Poroshenko's delay in putting forward a candidate following the resignation of the former governor last May caused concern to Ukraine's backers including the International Monetary Fund.