Mali, Burkina Faso and Niger are all under military rule following coups.
In January, the trio announced they were quitting The Economic Community of West African States, which they said was under French influence, to create their own regional grouping -- the Alliance of Sahel States (AES).
Faye landed in the Malian capital on Thursday and headed to the presidential palace where he is due to hold talks with junta head Colonel Assimi Goita, a Malian presidential source said.
"These visits are part of a drive to strengthen the historic ties of good neighborliness, fraternal friendship, solidarity and multifaceted cooperation," the Senegalese presidency said in a statement.
Faye has made several trips across West Africa since being sworn in as the continent's youngest elected president in early April.
Thursday's trip marks his tenth visit to an African state since assuming the presidency.
The choice of destinations within the continent "speaks volumes about the importance of strengthening pan-Africanism and reinvigorating sub-regional integration in his diplomatic priorities," a Senegalese government statement said.
Faye, 44, was elected on a promise of radical change and has said he wants to bring Mali, Burkina Faso and Niger back into ECOWAS.
Ghanaian President Nana Akufo-Addo has urged Faye to use his goodwill within the bloc to help resolve disputes with the three states.
Faye travelled to Guinea on Saturday where he met with General Mamady Doumbouya, who seized power in a September 2021 coup.