The Daily Nation, quoting a coastal police official, said the six Kenyans and the Nigerian were arrested on the small island of Lamu as they boarded a speedboat with the intention of reaching nearby Somalia.
The men were in possession of materials promoting jihad and allegedly admitted they had been radicalized by an imam at a mosque in the coastal town of Mombasa.
Insurgent group al-Shabaab is fighting to oust the Western-backed government in Somalia. Hundreds of foreign fighters are believed to back the group, which carried out a suicide bomb attack in Uganda in July.
Kenya has a significant Muslim population, as well as a large Somali diaspora.