Frenchman Alain Giresse resigned from the position on January 29 after the Teranga Lions crashed out of the 2015 Africa Cup of Nation in the group stage, citing threats, insults and pressure from the local press, officials and fans.
Former Burkina Faso coaches Paulo Duarte and Paul Put, as well as Michel Dussuyer, who led Guinea to the 2015 Afcon and Patrice Neveu are all vying for the job, according to the body.
José Anigo, Frédéric Antonetti, Luiz Fernandez and Jean-Pierre Papin, all from France have also submitted CVs, as well as Michel Pont from Switzerland.
The list also includes local coaches Amara Traoré, who managed Senegal between 2009 and 2012, Aliou Cissé, Lamine Dieng and Oumar Diop.
The Senegal FA says it is expecting more applications before the closing date. The successful candidate will be announced on March 1.