The Scot has won two clay court tournaments in a row, the Munich Open and on Sunday he won the Madrid Open hammering Rafael Nadal in the final.
"It's not impossible," Murray said of his chances of reaching the final or winning at Roland Garros.
"Whereas, maybe the last few years, even though I played some good tennis in Paris, I didn't feel like I was maybe healthy enough or played enough matches or had enough big wins against top players to believe I could do it.
"Maybe this year will be different. There's a chance. If I play well, then I know I have the chance to go far in the tournament," he added.
Murray takes on Belgium's David Goffin in Rome on Thursday hoping to rack up an 11th straight win on clay.