Hamilton, 33, won the fifth World Championship of his career last season.
And 31-year-old Vettel believes if the older Brit can still compete for the top honours then so can he.
The pair are expected to battle at the front of the grid for this year’s world title.
Vettel is also out to try and end Ferrari’s 12-year drought for the top motorsport honour.
“I think it’s clear that I’m not in the spring of my career anymore,” Vettel told Sport Bild.
“On the other hand, at 31 I still have plenty of time in this sport.
“Looking back, Michael [Schumacher] was even a bit older than me when he won his first title with Ferrari. And Lewis is two years older than me.
“I still have no thoughts of retiring.
“On the contrary, I’m doing everything to fulfil my dream of the title with Ferrari.
“And as far as my family is concerned, they support me and don’t get in the way.”
Vettel has not won the Championship since since 2013, when he scooped his fourth in a row with Red Bull.
And the German was asked if he has since ever thought of throwing the towel in.
“Not really or no, the answer is no!” Vettel replied.
“Because throwing in the towel would mean dropping everything and giving it up.
“No, because my goal, my dream is to become a Ferrari World Champion. It also motivates me that Ferrari is the biggest brand in Formula 1.
“For me it would therefore be the ultimate if I could win the World title with Ferrari.”