Photo credit: Red Bull GEPA
The reigning world champion, and likely back-to-back 2011 title winner, already has a deal with the dominant team to the end of 2014.
But Dr Helmut Marko has revealed to Sport Bild that he wants to add a further two seasons to the contract.
"We made a contract with Sebastian to 2014 because both sides assumed that we would have two years together under the new engine rules. That has now changed," said the Austrian.
Marko is referring to the fact that, subsequent to the signing of Vettel's 2014 deal, F1 decided to delay the debut of the new engine regulations from 2013 to 2014.
"That is why we have also extended the agreement with our engine supplier Renault to 2016," he explained.
Vettel has expressed the desire to one day switch to Ferrari or Mercedes, but Sport Bild quotes him as sounding open to extending his Red Bull stay beyond 2014.
"I feel very, very comfortable where I am at the moment and there is no reason to change. We're like a family," said the German.
