Paddy Power has Monk as short as 15/8 to succeed the struggling Welshman, whose future is under increasing pressure.
The recently sacked ex-Monaco boss Leonardo Jardim is 3/1 to lead the Saints next, ahead of David Moyes (15/2), Sam Allardyce and Steve Bruce (both 10/1).
Monk spent eight years on Southampton's books as a player and has since managed four clubs, Swansea City, Leeds United, Middlesbrough and Birmingham, with varying degrees of success.
The 39-year-old took the St Andrew's reins earlier this year and has led the Blues away from relegation danger and into the comfort of mid-table.
But whether he would leave that job so soon for Southampton remains to be seen, with the Saints dropping into the Premier League's bottom three after Saturday's defeat against Fulham.
Bruce, the former Birmingham and Aston Villa manager, had led the betting until Monk's sudden emergence.
Would the Birmingham boss be a good fit for Southampton?