The source, speaking on condition of anonymity, said the court in Manama rejected an appeal by Rajab's attorneys.
Rajab, a leading figure in protests that erupted in 2011 during the Arab Spring, was sentenced in July to two years in jail for press statements deemed insulting to the government.
Amnesty International has called the Rajab sentencing "a flagrant violation of human rights and an alarming sign that Bahraini authorities will go to any length to silence critics".
Home to a majority Shiite Muslim population, Bahrain has been ruled for more than 200 years by the Sunni Al-Khalifa dynasty.
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The tiny kingdom, located between Saudi Arabia and its arch-rival Iran, has been rocked by unrest since security forces cracked down on Shiite-led protests in 2011 demanding a constitutional monarchy and an elected prime minister.
Authorities have since tightened their grip on all dissent. They accuse Shiite Iran of backing the protesters and inciting unrest in Bahrain, a charge Tehran denies.