Vettel's current contract runs to the end of 2014, while Webber's deal is for this year only at present.
Briatore believes Vettel's decision to pass Webber for Malaysian Grand Prix victory despite Red Bull ordering them to hold station with the Australian ahead destroys the relationship between the team-mates and could cost them the championship.
"I think there's no relationship anymore," Briatore told RAI Radio.
"It was already very formal beforehand between the two Red Bull drivers, that was very clear last year.
"Now Vettel says he will help Mark, but Mark doesn't need any help. He should have won the race, and it's possible that Vettel will win every other race.
"I don't think this relationship can be fixed. They are two professionals, they will win races and so on, but it's unthinkable that Mark may help Vettel in the future and I don't think Vettel will help Mark.
"So we'll have two enemies inside a single team, and this will hopefully advantage Ferrari."
Asked if he now expected Webber or Vettel to leave Red Bull after 2013, Briatore replied: "That's for sure. Last year, already, there were problems.
"Their car is very competitive so drivers want to stay there, but [Sepang] was proof that no one is in charge at Red Bull.
"Vettel is the boss there. You can't have a team manager also doing the driving."
Briatore accused Red Bull team boss Christian Horner of weakness, alleging that the power balance between Horner, technical director Adrian Newey, Red Bull advisor Helmut Marko and company chief Dietrich Mateschitz is flawed.
"If there was a manager with balls, he would have had them switch positions again," said Briatore.
"The problem is that there are two people with different ideas on the pit wall, with Helmut behind them doing the talking with Mateschitz, so you understand they are all scared."
He also criticised the fact that Newey was on the podium rather than Horner.
"Normally the team principal goes on the podium at the first race win of the season," said Briatore.
"Christian didn't even have the strength to get on the podium - because they're terrified with a driver in charge instead of the team manager. You'd first go yourself if you win the championship or the first race, and after that you'd send race engineers or your technical director.
"The fact that Christian didn't go on the podium after scoring a one-two says a lot about his weakness compared to the others."
While, Lewis Hamilton says Red Bull only has itself to blame for the 'multi 21' team orders controversy at the Malaysian Grand Prix.
The 2008 world champion believes the team's favouring of Sebastian Vettel, even if the German does not officially have number one status, has led to the simmering tension between the German and his team-mate Mark Webber.
Vettel and Webber's relationship has soured before, notably in 2010 when they crashed in Turkey and three races later when the team took a new front wing design off Webber's car and handed it to Vettel.
Webber then ignored an order to hold station a year later in the British Grand Prix.
"Red Bull has a clear one and two, they always have. And that is why they have always had the problems they have had," Hamilton said.
"We don't have a one and two at Mercedes. I have always said, from the moment I was speaking to the team, that I wanted equality [with Nico Rosberg].
"They didn't offer me to be favoured but I just wanted to make the point that I am not a driver that comes and requests that like a lot of other drivers do."
Hamilton said that insistence on equality was one of the reasons he did not rejoice in his Malaysian podium.
The Briton was the beneficiary of team orders when Mercedes instructed Nico Rosberg to back off in the closing laps of the race.
"You have to be able to look at yourself in the mirror [and say] you won fair and square," Hamilton explained.
"In Malaysia I don't feel like I won my spot fair and square. Although I did drive a decent race, I don't feel spectacular about it."