French clubs Clermont, Toulon and Racing Metro are interested in signing Warburton when his contract expires at the end of the season.
"I've told Cardiff and the WRU that I want to extend (my contract) and sign here," he told BBC Radio Five Live's Sportsweek programme.
"I'm awaiting an offer. I haven't received anything yet, but that's my preferred option at this moment in time."
Warburton's future is linked to the turmoil that has engulfed the Heineken Cup with the Blues unable to offer a new contract until they know what revenue they will receive from European competition next season.
The Welsh Rugby Union had suggested they would centrally contract their top players such as Warburton and full-back Leigh Halfpenny to keep them on home soil.
Warburton has lost patience with the dispute over Europe.
"It's going around in circles and nothing seems to be getting resolved," the 25-year-old openside said.
"It's got to the stage now where I don't want to know anything about the European situation until it's resolved.
"Without sounding disrespectful, it's almost bored me. I don't know what's going and don't have any control over what happens.
"It's a waiting game and as soon as anything happens I'll be keen to know, but until then I'll just forget about it."
- Sports & Recreation