Cavendish's hopes of breaking the record for stage wins on the Tour ended cruelly on Saturday when he crashed out of this year's race, which he has long said would be his last, and broke his collarbone.
The world's most decorated sprinter announced in May that he would end his 17-year professional career at the end of the season.
"Yes, we want Mark to go on to 2024 and race his 15th Tour de France to win his 35th stage," Vinokourov told L'Equipe.
Cavendish has racked up 161 career victories, including 34 at the Tour de France to equal the record of Belgian great Eddy Merckx.
"I myself suffered a fractured femur in 2011 on the Tour and it was supposed to be my last year but I didn't want to stop just like that," said the 49-year-old Vinokourov, who was a gold medallist at the 2012 London Olympics.
"I stayed on and fought hard to win the Olympic Games in London the following year. Mark has the same mentality and the same determination to achieve his ultimate goal. We're ready to give him that opportunity. But it's up to him."
