Despite its financial troubles this season, Sauber's two vacancies would appear the most attractive of the few remaining places on the 2014 grid.
The Mexico-backed, 22-year-old Gutierrez had a troubled start to his F1 career last year, but he made progress as Sauber improved its car in the second half of the season.
He told Brazil's Totalrace that he would give himself a mark of 7 out of 10 for the season.
It is even rumoured that van der Garde visited Sauber's Hinwil headquarters this week.
Asked about his own negotiations for 2014, Gutierrez answered: "We're working hard.
"I think there are good opportunities for me to continue in formula one -- I hope things work out.
"For me, the priority has to be Sauber. I think it is important in formula one to have continuity, but it is always good to leave all the doors open."
Book discounted tickets and reservate your hotel room in our F1 Tickets Shop.