The 25-year-old joined Scarlets from Irish outfit Leinster in 2016 and he has developed into a key figure with the reigning PRO12 champions.
Beirne's performances have led to reported interest from his homeland but Scarlets are keen to ensure he remains on their books.
Pivac confirmed a deal is on the table and insists he could force his way into contention for an Ireland call in the future if he continues to perform consistently.
"We've spoken to his agent and to Tadgh and offered him an extension on his contract," Pivac said.
"He has a bit of a dilemma in that he is playing so well that all of a sudden there are some noises coming out of Ireland.
"I don't think they wanted to know him 12 months ago, and that's why he came here to the Scarlets to get some regular rugby.
"He's one we will continue to talk to and he has another big season coming up here.
"If he doesn't back up his performances from last season then there won't be any noises coming out of Ireland.
"He wants to play for Ireland and who can blame him? We'll wait and see how that one pans out."