Australian Webber confirmed at the Turkish Grand Prix in Istanbul nine days ago negotiations had started with the team in relation to an extension to his contract.
Coulthard feels there was an ulterior motive to the announcement, and he said: "Mark told the media over the Istanbul weekend that he had opened talks with Red Bull to extend his contract.
"If I try to rationalise why he would say that, I can only presume it was either to stimulate talks with the team or interest in the rest of the paddock, reminding people he's on the market.
"When you think about it logically, you do your private negotiations in private, and then when you've reached an agreement you make an announcement.
"You don't normally say, 'Er, I'm about to enter negotiations'. So I would conclude it was a positioning tactic rather than anything else."
If veteran Coulthard's theory is correct, Webber is undoubtedly in the ideal position after scoring all the team's points so far this season.
Coulthard has suffered a run of wretched luck, but if team boss Christian Horner is chasing points and performance, Webber is the man in the driving seat when it comes to a new deal.
With rumours Sebastian Vettel will step up from sister team Toro Rosso for next year, it appears likely Coulthard and Webber are fighting it out for the remaining race seat.
Yet speaking in his column for ITV, Coulthard is unwilling to play Webber's game.
He added: "As far as my own situation goes, I will keep my own counsel until I have a firm deal to announce."