De Jong has a hamstring injury, picked up on international duty with the Netherlands last month, and is out of Saturday's home game against NAC Breda.
Iceland international Sigthorsson has returned to training after an ankle injury but worked apart from the rest of the first team on Wednesday, Ajax said on their website (www.ajax.nl).
Ajax will be keen to get both back to bolster their chances in their final Champions League Group H match at the San Siro, which they must win to qualify for the knockout phase.
Barcelona, top of the group with 10 points, are already through, but Milan, second on eight points, and Ajax, on seven, will fight it out for the second qualifying spot. Celtic have been eliminated on three points from five matches.
Ajax were boosted last weekend by the return from injury of Bojan Krkic, the forward on loan from Barcelona. He scored in their win over ADO Den Haag on Sunday, a game missed by both De Jong and Sigthorsson.
Ajax are second in the Dutch league, two points behind leaders Vitesse Arnhem.