The 25-year-old joined Scarlets from Leinster in 2016 and he has tied down a regular spot in the starting XV under Pivac.
However, the County Kildare man has ambitions to represent his home nation of Ireland and Pivac admits he could move on to turn his dreams into reality.
Beirne played a huge role in helping Scarlets to lift the Pro 12 title last term and although Pivac admits his departure would be a blow he believes they will be able to find a replacement.
Pivac said: "We would love to keep Tadhg, but he has got burning ambitions to play for Ireland like all our Welsh boys have to play for Wales and that is the way it should be.
"Part of it will be out of our control, but certainly we will be looking at other players as well.
"Tadhg came in from outside so if he were to go I am sure we will find someone to replace him."