Martin O'Neill and Roy Keane are among those being linked to the vacant Southampton job.
The Saints are looking for their fourth manager in just over two years after sacking Mark Hughes.
The former Manchester City and Wales boss was in charge of the club for eight months before parting company with the club.
He leaves them languishing in Premier League relegation zone following a run of 10 games without a win.
First-team coach Kelvin Davis will lead the team against Tottenham at Wembley on Wednesday.
Southampton FC said in a tweet:
"We would like to express our thanks to Mark and his staff for all for all of their efforts during their time at St Mary's.
Former Watford and Espanyol manager Quique Sánchez Flores is said to be the favourite to take over, although reports claim Ralph Hasenhuttl, who left R-B Leipzig in the summer, is Southampton's preferred candidate.
Meanwhile, Stephen Kenny says he has no issue capping League of Ireland players.
#SaintsFC can today confirm it has parted company with First Team Manager Mark Hughes.
Full statement: pic.twitter.com/EisJf8c2gb— Southampton FC (@SouthamptonFC) December 3, 2018
The new Republic of Ireland Under 21 manager will take over the senior team from Mick McCarthy after Euro 2020.
The former Dundalk boss feels there is a wealth of talent in the domestic game.
- Digital Desk