The doctors are loathed to put a time frame for his recovery, but typically an ankle ligament injury takes anywhere from 4-8 weeks to come right. The French Open starts in less than six weeks.
"I have completely torn my ligaments and they are not giving me too much as they know potentially I might try to push the boundary a little bit. But I am kind of going through the treatment and they said let's keep assessing it and we will see how it progresses," Venus said.
Venus knows he could miss the entire clay court swing but retains hope he could be ready for Paris where he achieved his greatest success with American Ryan Harrison in 2017, becoming a grand slam champion for the first time.
"I will just follow the advice of the doctors. I would love to be playing there but time will tell," Venus said. "They say if I do try and push things and make things worth I could end up with surgery and six months off. So it's about sensible and listening to my body at the same time."
The Kiwi number one has ranking points to defend having made the quarter-finals at this week's Monte Carlo Masters and next month's Madrid Masters with Klaasen last year. However the world number 14 is keeping positive.
"If I can get back and be healthy and have a few deep runs here and there, things can change pretty quickly."