Lee Johnson may not lead his side out at Wembley, despite the win over Fleetwood Town in the northern final of the Johnstone Paints Trophy
Barnsley have given permission for him to speak to Bristol City over the vacant managerial role there.
City sacked previous boss Steve Cotterill last month in a bid to stave off relegation from the Sky Bet Championship and want Johnson, 34, one of the youngest managers in the Football League, to replace him.
"Bristol City FC can confirm it has been granted permission by Barnsley FC to speak to its head coach Lee Johnson," read a brief club statement.
"The club will be making no further comment."
Johnson, who spent five seasons as a player with City before leaving the club in 2012, has been named Sky Bet League One Manager of the Month for January after turning round a dismal start to his first full season in charge at Barnsley.
The Yorkshire club were in the relegation zone at Christmas but have mounted a play-off challenge on the back of six straight league wins and booked a place at Wembley in the Johnstone's Paint Trophy final on Thursday night with a penalty shoot-out triumph at Fleetwood.
Barnsley said in a statement: "(On Friday) morning we gave permission to Lee Johnson to speak to Bristol City concerning their managerial vacancy.
"We gave this permission because we believe that the structures that we now have in place must be the key to our future success rather than dependence on a single individual.
"If Lee decides to stay with Barnsley Football Club we will be delighted, but if he chooses to move on, we will continue unabated with the plan we have in place for the progression of our club.
"We will provide further information in due course."
Johnson went agonisingly close to reaching the Premier League with City as a player in 2008 when the club lost in the play-off final to Hull.
He finished his playing career at Kilmarnock and became the League's youngest manager when appointed by Oldham in 2013 at the age of 31.
The former midfielder steered Oldham to safety in League One and the club were in ninth place when he left to become Barnsley manager the following season, replacing Danny Wilson as head coach at Oakwell in February 2015.
His father Gary used to be manager at Bristol City