Wainwright has made 127 appearances and consistently been Dragons’ stand-out player.
He was man of the match on Sunday in the 23-21 comeback victory against Lyon that ended a near year-long winless streak, making nine tackles, 14 carries and having several key moments on the gain line.
“We want to keep him here, he is a Gwent man and his performance last weekend showed how important he is, not only for Dragons but Wales,” said Tiatia.
“He is a beautiful man and inspirational in the way that he does things – he is uniquely Aaron Wainwright, he understands what he is about and what he brings. We want to keep him in the building.”
Dragons are keen to establish his plans for the future in the coming weeks before pressing on with recruitment in January.
The Rodney Parade club, who signed a new Professional Rugby Agreement with the Welsh Rugby Union in May, will have an increased playing budget of approximately £6m next season.
Wainwright’s main rival for the number eight jersey is currently Mackenzie Martin, who is on loan from Cardiff and is out of contract next summer.
Tongan international Solomone Funaki joined in the summer of 2024 but has not made a competitive appearance because of a serious knee injury.
With Dragons without a United Rugby Championship win since the opening weekend of last season, there is an acknowledgement that the squad needs to be strengthened in key areas.