The 22-year-old Mexican is tipped to also leave the financially-struggling Swiss team as Nico Hulkenberg.
Dec.5 (GMM) Esteban Gutierrez has leapt to the front of the queue to move from Sauber to Caterham for 2014.
Gutierrez's 2013 teammate Nico Hulkenberg has already announced his switch to Force India, and now the 22-year-old Mexican is tipped to also leave the financially-struggling Swiss team.
The Swiss newspapers Blick and Neue Zercher Zeitung separately report this week that Gutierrez has been spotted visiting Caterham's UK headquarters.
Last month, the Telmex-backed Gutierrez admitted he was not sure if he would be staying at Sauber for 2014.
"We'll see what's going to happen," he said.
"Obviously we have been looking to different options, even if my idea is to continue with Sauber, because we have been working on a good relationship for a long time."