The Australian is the only significant member of the championship-winning team who is not yet already signed up for the 2013 season.
But billionaire team owner Mateschitz this week backed Webber, 35, to return to Sebastian Vettel’s pace this year, insisting the pair will receive no more or less than equality in 2012.
At the same time, however, Webber was utterly dominated by Vettel last season, causing some experts to predict that Red Bull will replace him for 2013.
Indeed, Mateschitz said at the Jerez test last week that “Our primary goal is to put one of our juniors in the car”.
He told the German-language Speed Week magazine: “That’s one reason why we changed the drivers at Toro Rosso.
“Both (Daniel Ricciardo and Jean-Eric Vergne) are highly talented and have great potential, but the question will only arise if, for example, Webber stops at the end of 2012.”