Dumoulin suffered the injury during the Giro d'Italia, forcing him to withdraw from the race in its opening week, and has struggled to regain form since the incident.
Wednesday's time trial at the Criterium du Dauphine was a bit test of the 28-year-old's fitness on a route that he would expect to dominate, but he lost 47 seconds to stage winner Wout van Aert on the day, and says his performance was a concern.
If the knee doesn't improve, or I can't improve the form I have now, then it doesn't make much sense to me (to go to the Tour de France).
"I have certainly not closed that book yet, because it has improved in recent weeks," Dumoulin added. "But it's just not going fast enough for me.
"I know that it is not possible at all, realistically speaking, but it frustrates me that I cannot win any races at the moment."
The Dutch rider's knee still shows visible signs of swelling, while he has also revealed that the accident left him with a small fragment of metal still embedded in his leg.
The news of Dumoulin's possible withdrawal comes just a day after Chris Froome suffered a high-speed crash that ruled him out of the remainder of the season.
Other leading contenders Geraint Thomas, Egan Bernal, Nairo Quintana and Adam Yates remain set to start the Grand Tour on July 6.