Cole and Chase Hakken, 4 and 2 respectively, were taken from their grandparents' home north of Tampa Wednesday.
Police said they believed the boys were taken by their parents, Joshua Hakken, 35, and his wife, Sharyn Hakken, 34, who had lost custody of the children after Joshua's drug-possession arrest in Louisiana.
Police said the family then fled on a 25-foot sailboat from Madeira Beach, the Tampa Bay Times reported. Joshua Hakken was armed with a gun, police said.
The Hillsborough County, Fla., Sheriff's Office said Monday it had information the family had reached Cuba, WDSU-TV, New Orleans, reported.
The FBI and the U.S. State Department were working to confirm. that information, the TV station said.
2014: The Year in Music [PHOTOS]