Washington (CNN) The State Department is expected to recommend that Cuba be removed from the government's list of State Sponsors of Terrorism, a U.S. official told CNN on Tuesday, a notorious designation that has been a stumbling block in the establishment of embassies in both Havana and Washington.

"Our expectation" is that Cuba will be removed from the list, the official said. But the official cautioned the Obama administration has yet to make any formal announcement. While that announcement from the State Department is not expected Tuesday, it could come as early as Wednesday.

On a conference call with reporters, Deputy National Security Adviser Ben Rhodes said the State Department is "nearing its completion" of its review of the state sponsor of terrorism designation process. He did not rule out an announcement this week.

Cuba has raised the designation as a major objection in its talks with U.S. officials regarding normalizing relations between the two Cold War adversaries.

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