Team boss Cyril Abiteboul recently gave the Briton a hurry-up, amid rumours a mid-season driver change - potentially involving tester Sergey Sirotkin or even Robert Kubica - might be on the cards.
Palmer, who is yet to score a single point this year, said the rumours are not putting pressure on him.
"What puts pressure on is not putting in good performances," said Palmer.
"The way to stop the rumours is to do well on track and hopefully I can do that."
As for what has caused his 2017 struggle, however, Palmer said he isn't sure.
"I have no explanation," the 26-year-old is quoted by Speed Week.
"I don't think I've done anything wrong. There are just small things that make the difference," Palmer added. "I just have to drive as well as I can -- what happens on the other side of the garage doesn't matter."
He said F1 is now so safe that the grid is filled with pay-drivers.
"In the past, we were dealing with guys who were so passionate they were willing to risk their lives," Villeneuve told Die Welt newspaper.
"Now, fathers actually want their sons to race, even if they don't have the talent -- a formula one cockpit is safer than a motorbike or skiing," he said.
Palmer's father is British motor racing circuit mogul Jonathan Palmer, while Stroll's F1 career is funded by his billionaire father Lawrence Stroll.
Book discounted tickets and reservate your hotel room in our F1 Tickets Shop.
The cookie settings on this website are set to "allow cookies" to give you the best browsing experience possible. If you continue to use this website without changing your cookie settings or you click "Accept" below then you are consenting to this.