Carlos Tevez is enjoying his football in Italy and has every intention of honouring his contract at Juventus.
Ramires is hoping to spend 'much longer' at Chelsea after passing the 200 appearance mark for the club.
The Saints are 15th in the Barclays Premier League after coming back from 2-0 down to claim a draw with European champions Chelsea at Stamford Bridge on Wednesday.
But that was not enough to save Adkins from the axe, with 40-year-old Argentinian Pochettino taking charge of training on Saturday ahead of Monday's home game with Everton.
Saints executive chairman Nicola Cortese said: ""This decision has been made with the long-term ambitions of Southampton Football Club in mind.
"Whilst we acknowledge the contribution Nigel has made during the past two years, for the club to progress and achieve our long-term targets a change was needed.
"Mauricio is a well-respected coach of substantial quality who has gained a reputation as an astute tactician and excellent man-manager. I have every confidence that he will inspire our talented squad of players to perform at the highest possible level.
"He also shares my belief that the most successful clubs are built by nurturing young players through a development system that provides a clear path to the first team, thereby creating a culture that keeps them at the club for the long term.
"This is an approach he has employed with great success in the past and I look forward to him bringing that experience and expertise to Southampton."
Pochettino will take his first training session with the Saints squad on Saturday.
"This is the kind of opportunity that any coach would relish," he said in a statement.
"Southampton is a club with great heritage, and an even more exciting future. There is a clear vision to take the club to a new era of sustained success in the Premier League, and beyond, which I'm delighted to be part of."
Adkins joined Southampton from Scunthorpe in 2010 and he guided the Saints into the Premier League with back-to-back promotions.
Southampton started slowly on their return to the top flight but Adkins departs with the club three points outside the relegation zone after a run of just two defeats from their last 12 league games.
Pochettino has spent the majority of his football career at Espanyol, in two stints as a centre-back and then as manager between 2009 and 2012.
Pochettino won 20 caps for Argentina and it was his foul on Michael Owen at the 2002 World Cup that led to David Beckham scoring the match-winning penalty.