Sources report that the British driver and his father Jonathan turned down the French team's offer of $3m (£2.2m) to give up the seat to Carlos Sainz for the remaining six races of this year.
Indeed, Renault have now issued their official preview of this weekend's Malaysian Grand Prix, quoting Palmer as saying that he is looking forward to Sepang.
"The car keeps getting better, I'm certainly improving too so we'll aim to get another good result," he said.
However, there remains a chance that Renault could increase their offer to 'pay out' Palmer and his sponsors, amid rumours the driver's camp is pushing for a $7m (£5.2m) fee.
Yet Spaniard Sainz also seems confident that he will stay at Toro Rosso for Malaysia and beyond rather than do an earlier Renault switch.
"No-one has said anything about that to me," he told Onda Cero radio.
"I think it would be better to stay in Toro Rosso, completely focusing with the team on completing the season with good performances."
Renault sit seventh in the standings ahead of the race in Malaysia.