Browne was one of four players who had to pull out of the Republic’s Nations League game against Wales on Sunday after being deemed a close contact of a fifth player who tested positive for the virus.
The quartet fell into the close contact category having sat near the other player on the flight home from their Euros qualifier play-off in Slovakia.
When Browne had to pull out of the squad, North End hastily made arrangements to fly him home from Dublin.
Peter Ridsdale, advisor to PNE owner Trevor Hemmings, said: “The situation with Alan is frustrating.
“He played outstandingly well for us against Brentford and was excellent for Ireland when he came off the bench in Slovakia.
“We’ve not yet had total clarity on his availability. At first sight it looks like he might have to self-isolate for a period which would exclude him from the weekend.
“Having said that, Alan did take a test on Friday and tested negative.
“He took another test on Monday and we are awaiting the result of that.
“Alan is at home. By the time I started my lunch on Sunday he was in Ireland and by the time I started afternoon tea he was back home.
“There were a few phone calls in between and we made sure we got him back.”
The international break has been fraught with Covid issues for the Republic.
A member of their staff gave a positive test on arriving in Slovakia, that meaning two players – Adam Idah and Aaron Connolly – had to pull out of the Slovakia game having been sat near him on the plane.
That test was later found to be a false positive, hence Idah and Connolly having to pull out was unnecessary.
Then came the unnamed player testing positive, which saw Browne, former North End winger Callum Robinson, John Egan and Callum O’Dowda having to pull out of the squad.
Ridsdale said: “Alan happened to be sitting in the seats in front of the lad who tested positive.
“Our frustration is that we have a lad in our employment who has gone away on international duty and is suddenly not available.
“That is not how we want to prepare for a game.”
PNE striker Sean Maguire remains with the Irish squad ahead of Wednesday’s Nations League game in Finland.
Maguire was a late call-up, only joining the squad on Friday after their arrival back from Slovakia.