The Spanish pair have both admitted in recent weeks that they could be forced to depart the Spanish champions in search of first-team football.
However, Pique has claimed that 'all players have to fight for places' at the Catalan outfit.
"I understand what Tello and Montoya have said, but this is Barca and we all have to fight for places. The doors are always open for unhappy people to leave," Pique told reporters at a press conference.
Pique returned to Barcelona from Manchester United in 2008.