It MAY be available in future and was hinted it would be an action through one of the pet stables in EU. Not all pets well be able to come through either just the ones that are supported in compet.
The big setback I can see from this being added is if EU pets can be purchased in the compet game it is cheaper to skill them in compet then in EU so there would be no point to training in EU and bringing to compet. If things stay with the current easiness to train in compet I would only see newly tamed pets ever being brought to compet and then skilled in compet game. Although they may add ability to bring in some rarer pets only from EU play into compet even at lvl 1 to distinguish some sort of unique one way connection between EU and compet. I do not see pets from compet ever being able to go back to EU with how fast training happens in compets at least not being able to and preserving any levels obtained in compet anyways.