They have signed the talented New Zealand back on a "long-term deal" from Waikato Chiefs in his home country.
But Anscombe, 23, has a Welsh mother and, Holland revealed, has already met Wales head coach and fellow New Zealander Warren Gatland.
"We took the opportunity to introduce him to Warren and I know Warren has been in touch since," Holland said.Continue reading the main story
Richard Holland Cardiff Blues chief executive "It's probably a question posed for the Welsh Rugby Union, but we'd be keen to see him progress to international honours and play for Wales.
“We are in negotiations with Auckland to see if there's a potential early release, but it looks like early November”
"Gareth is a hugely talented player and he's got a huge future ahead of him, certainly with Cardiff Blues and who knows maybe he will go on and represent Wales as well if Warren decide that's a path for him.
"But he's a young man, he's still got some bits and pieces to learn and I'll leave that to the rugby guys to nurture and develop."
Anscombe will give the Blues a valuable place-kicking option following the departure of Leigh Halfpenny to Toulon.
He can play fly-half or full-back and has scored 268 points in his Super Rugby career.
But it is likely that Anscombe will not be available to play for Blues until Auckland finish their season.
"The ITM [Cup] finishes at the end of October so the latest will be after that," Holland added.
"We are in negotiations with Auckland to see if there's a potential early release, but at the moment that doesn't look likely so it looks like early November."