US officials traveling with Clinton, who will also meet Prime Minister Petr Nečas, said the Temelin nuclear project could create up to 9,000 American jobs and would help ease the nation's energy reliance on Russia.
Majority state-owned Czech firm ČEZ has applied to build two new reactors at its 2,000-megawatt Temelin nuclear power plant, which would be one of the largest public investments in Europe this decade.
Westinghouse, a unit of Japanese firm Toshiba Corp, is competing with Russia's Atomstroyexport, which is bidding in a consortium with a Russian-owned Czech group.
"We are not shy about pressing the case for Westinghouse to expand the Temelin nuclear power plant, because we believe that company offers the best option for the project in terms of technology and safety," Clinton said in a news conference after meeting with Czech Foreign Minister Karel Schwarzenberg.
"So we clearly hope that Westinghouse will receive the utmost consideration as this process moves forward."
ČEZ, central Europe's biggest energy group, with a market capitalization of €13.6 billion, wants to pick a winner and sign a contract by the end of 2013.
ČEZ threw out a bid from France's Areva in October, saying the company failed to meet "crucial requirements". The Czech anti-monopoly office has said ČEZ cannot sign a contract until it rules on Areva's appeal.
US officials said formal negotiations between the two bidders and the Czech government are expected to start this month.
The United States is stressing Westinghouse's safety record, given concerns about nuclear reactors following the Fukushima disaster in Japan last year. Officials will also underline the advantage of reducing the Czech Republic's reliance on Russia for energy.
Clinton will also discuss energy security with EU officials in Brussels on Wednesday.