Podolski, 26, has been strongly linked with a move to the Gunners at the end of the season after expressing frustration with life at Cologne, who are currently 14th in the Bundesliga.
Fellow Germany international Mertesacker, who left Werder Bremen in the summer, has now said Podolski has been in touch.
"He has shown a lot of interest in recent weeks and has sent me a text message," Mertesacker told Sky. "As you can imagine, I've told him positive things."
Asked whether a deal was done, he said: "I haven't been told that, and Lukas hasn't called me. I have written to him, though, to tell him how well he can do here and what a great club it is. I think it can happen."
Meanwhile, Mertesacker remains hopeful of recovering from injury in time to help Arsenal in the run-in and represent his country at Euro 2012.
He underwent ankle ligament surgery last month and was expected to be out until the summer, but he said: "I hope I can still play this season."