Defending champion Carlos Alcaraz says the results of the next test on his injured wrist will be "crucial" in determining whether he plays at the French Open.

The world number two pulled out of the Barcelona Open last week after sustaining an injury to his right wrist in his first-round victory, and later withdrew from the Madrid Open, which starts on Tuesday.

Seven-time Grand Slam champion Alcaraz, who has won back-to-back French Open titles, has described the injury as "more serious than any of us expected".

The French Open runs from 24 May to 6 June.

"We've been trying to do everything we can to make sure that this test goes well," Alcaraz told Spanish television channel TVE.

"I'm trying to be very patient. But we are good and just waiting a little bit.

"We have a few tests in the next few days, and then we will see how the injury is and what the next steps will be."

Jannik Sinner reclaimed the world number one ranking this month after beating Alcaraz in the Monte Carlo final.

Alcaraz, who won clay-court titles in Monte Carlo, Rome and Roland Garros and reached the final in Barcelona last season, could lose significant ground to Sinner in the rankings because of the injury.

"I'd rather come back a little later but in great shape than come back early, rushing around, and unwell," Alcaraz said.

"God willing, I have a very long career ahead of me - many years - and pushing myself too hard at this Roland Garros could seriously harm me in future tournaments.

"Things happen in the professional world. You have to accept them.

"I need to recover really well if I don't want it to affect me later on."