Earlier, boss Monisha Kaltenborn had said when asked about the performance of her drivers: "I am not satisfied with the performance of the team."
Esteban Gutierrez, however, appears safe. He is backed by Telmex, whose Carlos Slim is closely linked with the newly-confirmed 2015 Mexican grand prix.
And although Mexico City was initially scheduled for the 2014 calendar, F1's other Mexican driver Sergio Perez on Thursday insisted it will definitely take place next year.
"I have no doubt about it," he said in Hungary.
Unlike Gutierrez, Sutil's place at Sauber appears less secure, particularly as Dutch reserve driver Giedo van der Garde's sponsor McGregor is apparently offering "many millions" for his seat.
It is believed the switch could be made within the 2014 season -- and perhaps as soon as the forthcoming summer break.
The rumours were pushed along at Hockenheim when Sutil's manager Manfred Zimmermann was spotted in the Caterham motor home.
Was he lining up an alternative drive with Colin Kolles, Sutil's old Spyker boss?
Although out-sponsored at Sauber, Sutil nonetheless carries some backing -- and certainly more than Caterham's Kamui Kobayashi.
The Japanese said a week ago: "I cannot bring anything money-wise. It's fine to lose out to a driver with money -- this is formula one unfortunately."
But Sutil insisted at the Hungaroring on Thursday that his feet are firmly planted.
"I'll be here for much longer, so sorry -- you'll have to live with my face," he told reporters firmly. "Any more questions?"