Maskhadov's family reportedly appealed for asylum on "humanitarian grounds" in a letter to Finnish President Tarja Halonen.
Officials in Helsinki confirmed the letter was received this month but declined to give details.
Isa Akhyadov, a coordinator of the World Chechen Congress, a Chechen diaspora organization, said Maskhadov's family felt threatened in Baku, where they currently live.
Maskhadov's family also say they have been granted refugee status by the UN refugee agency, the UNHCR.
Maskhadov was killed during an operation by Russian security forces in March 2005.
(Ekho Moskvy, Interfax, AP)