Speaking to the Canadian Press (via CFL.ca), Alouettes interim head coach and general manager Kavis Reed said the team has had "no conversation" about signing Kaepernick.
Reed did note the Alouettes called Kaepernick's camp "to let them know we had his rights and if there was anything they were interested in to get back to us."
Reed said they have not received a call back from Kaepernick's agent.
On Tuesday, Reed told reporters following a team practice that Montreal was doing its homework on Kaepernick.
"He's in the midst of some very important things," Reed said. "We understand there's a movement going on around him. We're doing our due diligence and making certain they know we want to see where he's at. It's a matter of kicking the tires at this stage."
Montreal is struggling through a poor 2017 season with a 3-10 record, worst in the CFL with five games left to play.
Kaepernick has been a free agent since opting out of his contract with the San Francisco 49ers in March. The 29-year-old has generated little interest from NFL teams over the past six months. He had a meeting with the Seattle Seahawks in May but did not receive a contract offer.