Both are now advisers in President William Ruto's office. The shortlist of six was published late on Tuesday by the Public Service Commission, which is leading the recruitment.
The post will become vacant in June when Governor Patrick
Njoroge's tenure ends after eight years.
Thugge was a senior staffer at the International Monetary
Fund in Washington before joining government, while Mohamed
served as a chief executive of Barclays Bank of Kenya, now Absa
Bank.
They will face off for the post with four others, including
the current head of the debt office in the finance ministry, and
a former head of planning in the finance ministry.
The next governor will face a challenging task due to a
heavy government debt burden, which is threatening to upend
years of macro stability.
They will also have to deal shilling currency's sharp
depreciation, which has been partly blamed for inflationary
pressure.
All six candidates will be interviewed by the commission on
Tuesday next week, which will then forward a shorter list of its
preferred candidates for the president to choose from.
(Reporting by Duncan Miriri; Editing by George Obulutsa & Simon
Cameron-Moore)