Team principal Monisha Kaltenborn has confirmed a solution to Sauber's recent financial problems is close, with fresh investors due to come on board soon.
The current lack of resources has severely limited development to the C35, leaving the squad without a point after 10 races.
Brazilian Nasr is adamant he has confidence in Sauber, however feels the team has to first show its commitment before sorting his own future.
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Asked by Autosport whether he felt he would have to prove himself to the new investors, Nasr replied: "I need to see what I want as well, if I want to stay, and if I can clearly see the team has something to believe in.
"I do have faith in the team. I've believed in them, even from last year, when I had a really good start to the season, my first season in Formula 1.
"I know the difficult times they have had, which is all related to one thing, which is the development, the financial situation. We have struggled.
"From my side, I still have faith here, if we get the things together.
"If so, then I'm sure it can be a place I can perform well."
Nasr believes he can do no more with the tools at his disposal, and he feels he has been proving himself of late.
"I have been showing the little things I can do," added Nasr.
"In the British Grand Prix I set the fastest lap of the race at one point, and I was fighting with a Williams.
"In the previous race in Austria I was in the top 10, and in Baku as well I was fighting with a McLaren.
"So all I can do as a driver is show [what I can do]. That's what I can focus on."
Nasr feels with fresh investment, and new parts, Sauber can end its points drought, having also failed to score in the final three grands prix of 2015.
A new rear wing that was tested in practice in Silverstone is due to make its race debut in Hungary, while there is also a new front wing in the pipeline.
"As the races go by you can see the other teams are going forward, and we are pretty much where we have always been," said Nasr.
"But we can still fight for the next 11 races. There are still plenty of races to go.
"It's about getting the car at the right level of performance, getting the updates to work. I don't think we are too far from scoring a point."
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