The Briton, who is Lotus’ reserve driver, made his F1 free practice debut in China and will be in the car for the first session again in Bahrain on Friday.
Palmer’s current deal with Lotus will see him taking part in “a significant number” of free practice sessions throughout the season.
However, he admits having the chance to race elsewhere in between his F1 commitments would only prove to be beneficial.
“If I get a good offer to do something that would be a good career move for me then I’d like to race,” he told AUTOSPORT.
“It’s about keeping sharp. It’s the one thing I’m missing this year.
“I’m loving working with Lotus and being in F1, but I’d love to be racing as well, so if I get a good offer I’d love to.”
Palmer said he is not actively seeking a drive in another series and any potential opportunity could not impact on his Lotus role.
“My main priority is Lotus and I will not compromise anything I do here by racing elsewhere,” he said.
“But if there is something that came along that could fit in with this role then I’d be happy to do it.”
Looking ahead to the rest of the season, Palmer says his focus is to prove he is good enough to get a race seat in the future.
“I want to be really pushing the race drivers,” he said. “That’s the aim.
“I’m pretty much running on the same run plan.
“It’s not like we’ve seen in FP1 sessions before with other drivers where they have been on qualifying settings, engine turned up or low fuel.
“There’s a direct comparison, so I want to show why I should be racing next year.”