Rafael Nadal conceded he is "living with an injury" after suffering his earliest Internazionali d'Italia exit since 2008 against Denis Shapovalov, but still hopes to compete at the French Open later this month.

Record 21-time grand slam winner Nadal fell to a 1-6 7-5 6-2 defeat to Shapovalov in the third round in Rome on Thursday after struggling with a foot injury throughout the match.

The 35-year-old could be seen regularly limping and battling through the pain, but his resistance ultimately wilted as the Canadian surged to victory after winning 12 straight points from 2-2 in the deciding set.

Nadal, speaking after the defeat, detailed the struggles he is having on a day-to-day basis as injury problems continue to hamper him.

"I am not injured. I am living with an injury. My day-by-day is difficult," he told reporters.

"I am trying hard but of course, it's difficult to accept the situation at times. A lot of days I can't practice the proper way.

"It started halfway through the second set and it was unplayable for me. [But] I don't want to take away credit from Denis that he deserves."

Asked about his chances of being fit for the French Open, which starts on Sunday, May 22 at Roland Garros, the Spaniard responded: "[It's] still the goal, in one week and a couple of days. I'll still keep dreaming.

"Maybe in two days, things are better, the things that I have on my foot. It's true that during Roland Garros I'm going to have my doctor with me – that sometimes helps."

Defeat to Shapovalov also meant Nadal will drop to number five in the world rankings, leaving him facing a potential meeting with the top seed in the quarter-finals of the French Open, which he has won a record 13 times.