The players' agent Pavel Paska was at Loftus Road to discuss a potential move with the club's co-owner Flavio Briatore last week and is confident that an agreement can be reached.
Cerny has been preferred to England 'keeper Paul Robinson of late, making eight appearances for the club in all competitions this season.
The Czech international is at White Hart Lane on a long-term loan deal from Slavia Prague but that contract is due to expire at the end of the season.
Czech Under-21 international striker Pekhart has impressed for the club's youth team and it is felt the opportunity to play regular football at a competitive standard would help his development.
"QPR want to capture both players in the January transfer window," Paska said on the International Sport Management website.
"Radek's contract with Tottenham expires in the summer, while Pekhart could leave on a six-month loan with an option for a permanent move at a later date."