Gatland, who Pivac succeeded as Wales boss after the 2019 World Cup, could potentially step in as interim head coach on a 12-month contract, the PA news agency understands.
It is thought that a number of previously unscheduled meetings involving senior Welsh Rugby Union figures have taken place following an embarrassing home defeat against Georgia eight days ago.
And while no decision on Pivac’s future has yet been made – a review of Wales’ dismal Autumn Nations Series campaign could take at least a week – his time appears to be up after 34 Tests in charge that delivered 13 wins, one draw and 20 defeats.
The latest loss, a 39-34 reversal against injury-hit Australia after Wales conceded 26 unanswered points during the final 22 minutes, was a ninth defeat in 12 Tests this year.
Pivac was due to travel to France on Sunday for a World Cup reconnaissance mission, assessing Wales’ four pool-stage venues of Bordeaux, Nice, Lyon and Nantes.
But whether he is in charge for the tournament appears increasingly unlikely, while Wales’ Six Nations opener against world number one team Ireland is less than 10 weeks away.
Pivac oversaw a Six Nations title success last year, when Wales were seconds away from winning the Grand Slam, and a first victory over the Springboks in South Africa, but the Georgia debacle came just eight months after a home defeat against Italy.
In contrast, Gatland’s 12-year Wales reign was studded with success and consistent performances.
Wales won four Six Nations titles during that time, including three Grand Slams, reached two World Cup semi-finals and briefly headed the world rankings.
Gatland is currently director of rugby at the Chiefs in New Zealand, but he has spent the last month watching autumn series games in his role as a pundit for Prime Video.
He was in Cardiff for three of Wales’ Tests – against New Zealand, Argentina and Australia – and is understood to be flying home later this week.
Speaking immediately after the Australia defeat, Pivac said: “We review every competition, and we will do that and we have to take the positives out of the competition. Things that did not go well we can iron out.
“I certainly want to stay. You saw when we get things right we are a dangerous team.
“We have more players to come back into the side and the rest is up to other people.
“I am contracted through to the Rugby World Cup.”
Former Wales star Jamie Roberts, though, does not believe that Pivac is the man to lead a World Cup campaign.
“Regardless of the (Australia) result, I am not quite sure we have seen enough to warrant him taking us to the World Cup,” Roberts told Prime Video.
“Obviously, he wants to stay, but I haven’t seen that performance regularly enough throughout the last 12 months to convince me that Wales can have a shot at winning the World Cup.
“Test match rugby is about winning, regardless of how you play. It is a results-driven business, it’s professional sport.
“I look at this objectively, and this year we have lost at home to Italy and Georgia for the first time in our history.
“If we want to dine at the top table of international rugby, that is not acceptable.”