Palmer is due to fall out of contract at the end of the current campaign and his struggles have led to speculation the team will seek a replacement.
The British driver has so far failed to pick up any points and has been outperformed by team-mate Nico Hulkenberg, who sits 10th in the drivers' standings with 26 points on the board.
Reserve Sergey Sirotkin and development driver Oliver Rowland have been mooted as potential replacements and there have also been suggestions Robert Kubica could make a sensational return to F1 full-time following a serious injury.
However, Renault managing director Cyril Abiteboul says the team have not ruled out the possibility of retaining Palmer if he can improve when the season resumes after the summer break.
"Frankly, if he manages to turn around the situation, which he did last year, we are completely open to a future between the team and Jo for one more season," Abiteboul told Autosport.
"Stability would be good for the team. That's also what we wanted last year - to have Nico changing we wanted not to have to change two drivers.
"Things could go his [Palmer's] way, but at the end of the day that's in his hands.
"He knows that right now he's on a one-year contract and completely understands the team has to assess its options for the future."