Cotterill, 53, was only appointed in September but his reign is understood to have ended following Saturday’s 2-1 Sky Bet Championship loss – a fifth straight defeat – at Nottingham Forest.
The result left Blues third from bottom in the table, two points from the safety line, and hunting their third permanent manager of the season.
Press Association Sport understands Birmingham’s board wants to turn to Monk,with the 38-year-old still available since leaving Middlesbrough in December.
He wants to get back into management and Blues, who have kept tabs on the Welshman ever since he left Swansea in 2015, are ready to offer him that chance.
The Championship outfit have also held talks with former Scotland boss Gordon Strachan, despite the 61-year-old being out of club management since 2010.
Cotterill only took charge of Blues last September, penning a two-and-a-half-year deal worth around 450,000-a-year.
But he has struggled to turn things around, winning seven of his 27 games.
Further questions over his future were raised on Saturday when there was no Birmingham presence in the Nottingham Forest boardroom.
Press Association Sport understands Birmingham, owned by Chinese firm Trillion Trophy Asia, opted to have a private box for the game at the City Ground.
Cotterill, who said he had positive talks with the club’s owners this week, replaced Harry Redknapp after the former Tottenham boss lasted just 13 games.
Redknapp was drafted in for the final three games of last season – with Cotterill his assistant – and guided Blues to safety, banking a 250,000 survival bonus.
He was given 20million to spend in the summer, breaking the club’s transfer record by signing Jota from Brentford for over 6million, but left after only 10 games of this season.
Swansea boss Graham Potter admits players will be moved on and anyone who does not want to stay will be allowed to go.
New Swansea boss Graham Potter insists he will 'take the lead' on recruitment as he looks to strengthen his squad this summer.
Arsenal have confirmed Freddie Ljungberg has been appointed as head coach of the Gunners Under-23 side.
Antoine Griezmann says he has made a decision on his future, but refused to clarify where he will be playing his football next season.