Barclay suffered a shoulder injury in Scotland's 22-16 defeat by France on 12 February and came back to his Welsh region for a medical appraisal.
Pivac said the signs were promising after a scan on the injury.
"It was a good scan. He's getting treatment so fingers crossed he will be right for the Welsh Test," said Pivac.
"He goes back to Scotland now and they will be in charge of his recovery from here. It will be their call.
"But certainly it was nowhere near as serious as first thought."
Scotland are already without captain Greig Laidlaw (ankle) and number eight Josh Strauss (kidney) who have both been ruled out of the tournament.
There are also concerns over flanker John Hardie and hooker Fraser Brown who both suffered blows to the head in Paris.
And wing Sean Maitland was injured on Friday evening in Saracens' defeat by Gloucester in the Aviva Premiership.
A Welsh player who could be involved in Murrayfield - wing Steff Evans - scored the Scarlets' opening try in their 42-7 Pro12 win against Zebre.
Evans has not featured for Wales so far in the Six Nations, and impressed Pivac with his commitment against the Italian side.
"Steff was itching to get a run and he got his hands on the ball out there.  He will be better for that," added Pivac.
"Tonight's game was important for him, to get a blow-out.
"He has been in camp and training well and really enjoying it by all accounts.
"He will be happy with that 80 minutes under his belt."
Scarlets coach Wayne Pivac is hopeful John Barclay will be fit to play for Scotland against Wales in the Six Nations on 25 February.