Giovanni Trapattoni revealed on Thursday that the 32-year-old said he had an option to return to England over the winter, but Lambert denied any knowledge of the stories.
"When January gets closer, I'll start to think about things. Robbie Keane is a brilliant player and has been over the years," he said.
"Is it something I would go for? I am not sure because the team is the most important thing for me.
"If they fit in and have the desire to do it, and want to do it, and fit in with the group, then I will look at it.
"Signing an experienced player is not something I'll turn away from."