No concrete information but I am following this with interest and am aware of it as I go to Chester a lot. The current links are MAN and LPL. Neither has direct train services to Chester. MAN one change, LPL bus + slow suburban train. Taxi £40-60. BHX is another option and has direct trains but is a longer journey.
I do wonder though given the proximity of those three established airports if there is sufficient demand for services to Hawarden to be viable. Chester is a very attractive tourist destination, in fact was recently voted the fifth most beautiful city in Europe, and rightly so.