According to the paper, Finance Minister Samuel Mumbengegwi approved Gono's re-appointment on Tuesday, extending his time in the post to November 30, 2013.
A ministry spokesman declined to comment on the report.
Appointed in December 2003, Gono's term has spanned the economic collapse of once-prosperous Zimbabwe, highlighted by shortages of basic goods and the highest inflation in the world, which the government put at 230 million percent in July.
Washington-based Cato Institute foundation estimates Zimbabwe's inflation at 89.7 sextillion percent.
In an effort to deal with hyperinflation, Gono has introduced higher denomination notes and lopped a total of 13 zeros off the currency -- 3 zeros in August 2006 and 10 in August 2008 -- but it has continued to lose value.
Currently, the highest denomination banknote is Z$1 million, not enough to buy a loaf of bread and consumers have to carry huge amounts to make simple purchases.
Zimbabwe's economic crisis -- blamed on President Robert Mugabe's policies -- has worsened amid a stalemate over cabinet positions in a power-sharing government the veteran ruler agreed to form with opposition rival Morgan Tsvangirai on Sep. 15.
Analysts say the power-sharing pact offers the best chance of hauling the country out of its worst economic crisis, but hopes of a quick turnaround have been dimmed by a disagreement over key ministerial appointments, which now threatens the deal.