The Wales skipper was ruled out of the Lions tour after suffering a shoulder injury.
Wales skipper Jones, who has made a world record 157 Test match appearances, was due to captain the Lions in South Africa.
But a dislocated shoulder suffered just seven minutes into the Lions’ victory over Japan at Murrayfield last Saturday ended his tour hopes.
Jones’ fellow Wales international Justin Tipuric was also ruled out of the South Africa trip due to a shoulder injury picked up in the same game, with Lions head coach Warren Gatland summoning Wales forwards Adam Beard and Josh Navidi as replacements.
Jones, 35, agreed a contract extension earlier this year with the Ospreys and Welsh Rugby Union that runs until the end of next season.
Wales head coach Pivac said: “We are speculating a little bit here on how long Al will be out for, but if he were to be out for a lengthy period of time then the way I look at it is it’s miles on the clock you tack on the other end.
“At the end of the day, the focus for him and for us now is getting him right to play again.
“He has got to come to us and tell us what he wants to do, and knowing Al, I am sure he will get over the disappointment and work hard to come back, because he’s certainly got more in the tank as far as I am concerned.”
Ireland scrum-half Conor Murray was appointed Lions captain following Jones’ tour withdrawal.
But Pivac has no doubt that the decorated second-row forward – his Wales career is highlighted by five Six Nations titles, three Grand Slams and two World Cup semi-final appearances – will bounce back.
“Knowing Al, with the way he is, he will hit the refocus button, he will set a new target, whatever that looks like, and we will be across that shortly,” Pivac added.
“I think we all saw it with the knee injury he suffered in the Italy game at the end of the autumn.
“He had a window of opportunity where we were told that he would miss the first two Six Nations games (against Ireland and Scotland).
“The guy did everything humanly possible to get himself ready as quickly as possible, and he gave us a date that he felt he would be right. He was bang on (Jones started both games).
“He is a very strong character mentally, very tough, and if he sets his mind to something he will achieve it 99 times out of 100.
“If he says he is coming back from this particular injury and he gives himself a date, I wouldn’t bet against it.”