"They're going to be a major player in Europe," said Turner.
"They have kept their talisman (Xavier Rush) after the Ulster business and they have added quality players like Michael Paterson.
"I think they'll go all the way and I can see them doing well in the Magners League and in Europe. You need the type of squad they've got to go far in the Heineken Cup."
The Blues became the first Welsh side to win a European trophy when they lifted the Amlin Challenge Cup in May after beating RC Toulon in a stunning final in Marseille.
Dai Young's men now face former European Champions Northampton Saints along with Castres Olympique and Edinburgh in Pool One of the Heineken Cup this season.
Meanwhile, the Dragons will be looking to make it out of their pool and into the quarter-finals of Europe's premier competition for the very first time.
The Gwent region begin their continental campaign away to Glasgow Warriors on Friday, October 8 in a tough pool that also features current Heineken Cup Champions Toulouse and former winners London Wasps.