The inconsistent Danes, who have won only three of their eight games and suffered a shock 4-0 defeat at home to Armenia in June, host Italy on Friday before welcoming bottom side Malta on Tuesday.
"We have to admit we haven't been good enough, but we still have a chance to qualify and that's what is most important at this stage," captain Daniel Agger told Reuters.
The group situation is further complicated by the fact that Bulgaria, alongside Iceland in Group E, have the lowest points total of any second-placed side, meaning that even if Denmark do finish second they risk not even making the playoffs.
Eight of the nine second-placed sides will compete in the playoffs.
Olsen can count on the return of striker Nicklas Bendtner, who is back in the Danish squad following a six-month suspension imposed by the Danish FA (DBU) for his involvement in a drink-driving incident earlier in the year.
"What's done is done, and there's no point talking about it," said Bendtner.
"It's over. I'm the same footballer as before.
"It's great to be back, I've missed it an awful lot. It's great thing for a player to be involved with the national team."
Italy will be without Roma midfielder Daniele De Rossi, who was sent home from their training camp on Monday after team doctors discovered a tendon injury in his left thigh.
However, they are bolstered up front with the inclusion of Giuseppe Rossi, who makes his international return just over two years after he last played for the national team.
American-born Rossi has been plagued with knee problems since he first suffered a cruciate ligament injury while playing for Spanish side Villarreal in 2011, but he has started this season in blistering fashion for Fiorentina, scoring five goals in their first six games.
"I've learned not to not think too far ahead. Today's training, this season with Fiorentina, what I need to do to return to 110 percent of my physical condition: the World Cup comes after all this, and I need to get there in form, if I get there at all," he said.
"I've worked really hard to be here, but I never had any doubt that I would come back the player I was. In fact I've always believed that I would come back even stronger than before."