The Scottish Government will decide if Celtic players must self-isolate from Monday after the club’s winter training camp in Dubai.
Persons who have travelled back into the country from Dubai since January 3 are being asked to isolate for 10 days under new rules introduced on Sunday night.
Celtic, who play Hibernian live on Sky Sports Football on Monday night, are waiting for confirmation on whether they are exempt from isolation due to their elite sporting status.
The entire Celtic squad was tested upon arrival into Glasgow Airport on Friday and received the results on Sunday, with an unnamed player returning a positive result.
The Scottish champions said in a statement on Sunday: “Clearly the player will receive all our care and full support.
“All other members of our squad, management team and backroom squad are negative.”
A Scottish Government spokesman said: “We are aware there has been a positive case of coronavirus with Celtic FC.
“Scottish Government clinicians and the GGC Health Protection Team are in contact with Celtic providing advice on next steps.”
But he insisted the club did everything possible to mitigate risks of catching Covid-19 on their training camp and both the Scottish Government and football authorities were content with the measures they put in place.
Kennedy stressed they travelled on their own flight, stayed in a separate part of their hotel, and only ventured outside to go to training.
Celtic organised the trip in November and requested their match with Hibernian be moved to Monday.
The request was approved by the SPFL board, despite protests from Hibs.
“We just have to concentrate on ourselves,” said Kennedy. “We know we have put ourselves in a position which is difficult. We didn’t want to be in this position but it is what it is.
“We know there is not a lot of room for error now. We just have to attack it and do what we can.”
When asked if Celtic were capable of going on a 19-game unbeaten run with two victories against Rangers to win the league, Kennedy said: “It has got to be the mindset. There is nothing else for it.
“We have got to approach it as positively as we possibly can. We know the situation is difficult, we know the challenge, but we will never, never lay down and allow things just to pass.
Celtic will be without central defenders Shane Duffy and Nir Bitton for their Scottish Premiership clash with Hibernian.
Bitton is suspended following his Ibrox red card and Duffy will miss the game after leaving Celtic’s Dubai training camp early to deal with a personal matter. The Irishman will return to the squad after Monday’s game.
James Forrest remains unavailable but has stepped up his rehab work following ankle surgery.
Hibernian will again be without goalkeeper Ofir Marciano (calf).
But they have filled the void left by Marciano’s injury and Dillon Barnes’ return to QPR with new loan signing Matt Macey and Kevin Dabrowski, who was recalled from Dumbarton.
Kyle Magennis (hamstring) and Sean Mackie (thigh) remain out while Scott Allan is building up his fitness after illness.