Both drivers are fighting to secure their future in the team, with only one seat left and a number of drivers from outside the team also being linked with the drive.
"Fighting your teammate is quite tense for the battle for next year," Palmer told Autosport. "There's probably an extra element between the two of us to finish ahead.
"I'm still pushing to show the best I can and hopefully that's for Renault [next year], if not then I need to show the best I can for everyone else. There's a lot to play for. I hope it's not too late."
"Since the summer break, even going back to Budapest before the break, my performances have been much stronger," he said. "Every weekend now I'm right there, and the race pace is much stronger.
"I'm showing everything I can, and I hope it's enough. I'm pleased with my qualifying now to be on a really good run, and the pace in the last three races was good."
Bahrain International Circuit - Winter testing