The list also includes the German Volker Finke, Belgian coach Hugo Broos and Aliou Cisse, former captain of Senegal who played at Paris St Germain and Birmingham City, the Senegal news agency APS reported.
Cisse, 36, has worked with the Senegal national side and Olympic team as an assistant coach over the last year.
The 60-year-old Giresse, who played for France at the 1982 and 1986 World Cups, has extensive African coaching experience and earlier this year took Mali to third place at the African Nations Cup finals.
Santini, also 60, has not coached professionally since departing AJ Auxerre in 2006. He was manager of France from 2002 to 2004 and had a brief spell at Tottenham Hotspur directly thereafter.
Finke, 64, spent almost two decades as coach of Freiburg in the Bundesliga, a club who had always had a larger than average quota of African players. His last job was at FC Cologne.
Broos, 60, won the Belgian league with FC Brugge and Anderlecht and has coached in Greece, Qatar and Turkey.
The new coach replaces Joseph Koto, fired in October after Senegal failed in the African Nations Cup qualifiers, and will be tasked with helping the west African country qualify for the 2014 World Cup in Brazil.