With Sergio Perez moving on to McLaren, Slim - one of the richest men in the world - has picked his compatriot and GP2 race winner Gutierrez to be his successor.
"We are talking to Sauber for next season and we intend to continue together in 2013, obviously with a Mexican as a driver, which is Esteban Gutierrez", Slim told Cancha magazine.
Sauber has already confirmed Nico Hulkenberg for 2013, with Kamui Kobayashi's time with the team set to come to an end. Despite his podium in the Japanese Grand Prix, Kobayashi has reiterated his struggle to search for sponsors to retain his drive.
Gutierrez took part in practice for the Indian Grand Prix, setting the twentieth fastest time. The Mexican driver is also participating in this week's young driver test at the Yas Marina Circuit in Abu Dhabi and went fourth quickest on Wednesday, completing 93 laps.