Lindegaard had knee surgery in March but could still play at the June 8-July 1 tournament if he can prove his fitness.
However, Olsen told reporters he would not take any player who was not a completely fit.
"We must be thorough and we must have respect for the other players and not bring ones that are half-injured," he said.
"We will look at Lindegaard when we have a chance and after that we'll make a decision."
Arsenal's Nicklas Bendtner, who spent the last Premier League season on loan at Sunderland, was the only classic centre forward in the squad although Olsen intends to name three more players at the end of Danish Superliga on May 23.
Denmark must register its final squad with UEFA by May 29.
Roda JC's Mads Junker and Nicklas Pedersen of another Dutch Eredivise side, FC Gronigen, are among those in contention with Bendtner for a starting position in Poland and Ukraine.
The 1992 champions begin their campaign in Group B on June 9 against Netherlands in Kharkiv before moving to Lviv to face Germany and Portugal.