The pressure is on for the Brit who is still hoping to be retained by the French manufacturer next season alongside new recruit Nico Hulkenberg.
But with current team mate Kevin Magnussen and Manor's Esteban Ocon also vying for the position, Palmer is up against big opposition.
The British driver's performance level has gone up recently however, with a point-scoring 10th place finish achieved in Malaysia followed by a good run in Japan which Palmer was particularly happy with.
"I think it was a very good performance and we’re almost in the top half of the field on pure race performance now," he said.
"We had a good strategy and strong pace; everything is progressing a lot really. Had we had the same amount of people retiring from the race as there has been in previous outings, we would have been scoring some strong points in Japan."
Since its return to F1 as a fully works outfit, Renault has struggled to provide its drivers with a competitive car, but recently a substantial improvement of pace has materialised.
"We know a lot more about the car and something the team has done really well this year is develop every aspect of how we utilise the car on track.
"This includes how we use the tyres, how we look at strategy and so on. From myself, I feel stronger and more confident with every race and that’s what you expect in a first season.
"In Japan, we had good pace, good strategy, kept the tyres alive and that's what we've been doing quite well the last two races. We’ve managed to jump into the midfield.."
The RS16's improvement comes at a crucial time for Palmer who absolutely needs to perform and deliver another good result this weekend in Austin as he fights to remain in Renault's good graces, and perhaps even in Formula 1 altogether.
"The biggest pressure is in qualifying because it's all down to one lap," Palmer explained to Autosport.
"If you don't put the lap together you are out in Q1, which is what happened to me in Malaysia and Kev in Japan, so there's big pressure on us.
"In the race I sort of thrive on it a little bit more because it's not down to one lap. It's difficult with the pressure because we've got to show what we can do, to try and show the bosses.
"You can't make any mistakes, but you can't be too safe either or you're too slow, so it's a compromise. Without the pressure that your career's on the line, it's probably a little bit easier.
"Without pressure everything is kind of second nature, whereas for us there's occasionally an element of tightening up.
"It would be nice to be a little bit more relaxed. There's always pressure in F1, but to know your career is on the line, it feels like every second that passes."