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."
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