The Englishman has emerged as the bookies joint-second favourite alongside Ross County boss Malky Mackay and behind Michael Appleton to replace Shaun Maloney.
Mowbray, who managed Hibs between 2004 and 2006, spoke last week, ahead of Blackburn's final home game against Sheffield United about his future and his work life balance.
He confirmed there had been no “conversation, approach or discussions” over a new deal to remain at Ewood Park and revealed he had “decided” on his future.
Mowbray said: “All I can do is say that there’s been no conversation, no approach, no discussions and we’re a week away from the end of the season, so what do you want me to think?
“I don’t feel like I’m being disloyal saying anything other than it looks like I’m leaving because there’s no contract discussions and I’m out of contract at the end of the season.
“At this moment I don’t need to instigate anything, I’m clear in my own mind. I’m pretty relaxed. Why? Because I’ve got a life balance to get on with.
“I’m not sure I’ve had my work-life balance right.
“I commit a lot of time to this football club, away from my family and my kids, but I need to address that pretty soon.”
He added: “I’ve decided.”
Mowbray was a very popular Hibs manager before leaving for West Brom. He benefited from a stream of excellent academy graduates. Until last season, he was the last Easter Road boss to lead the club to a top three finish, which he did in the 2004/05 season.
The 58-year-old had a short spell as Celtic manager until 2010. Since then, he has held manager roles at Middlesbrough, Coventry City and most recently Blackburn where he has been boss for more than five years.