Mauricio Pochettino would consider an approach from Tottenham Hotspur to become their manager after the sacking of Tim Sherwood on Tuesday, but Southampton have opened talks with the Argentinian aimed at persuading him to stay at St Mary's.

The Tottenham chairman, Daniel Levy, is taking stock after parting company with the ninth manager of his 13-year tenure at White Hart Lane. Pochettino has emerged as his favoured candidate and the former Espanyol coach would be receptive to discussing the possibility of a move with Levy.

Pochettino's squad at Southampton stand to enter next season minus two key players, with Luke Shaw and Adam Lallana having informed the club of their wish to consider offers from Manchester United and Liverpool respectively. The pair, who have been named by Roy Hodgson in the England squad for the World Cup finals, are under contract until 2018. They have not asked for transfers but their moves can be viewed as the opening steps in what tend to become protracted affairs.

United have offered £27m for Shaw and Liverpool's bid for Lallana is £20m. Southampton do not want to sell either of the players who helped them finish eighth in the Premier League and, at the very least, they would be resistant to agreeing deals before the World Cup. Strong performances in Brazil could increase the players' values.

There is the feeling in Southampton that the sale of star players has to stop at some stage – the club have offloaded Theo Walcott, Gareth Bale and Alex Oxlade-Chamberlain in recent years, among others. The chairman, Ralph Krueger, is on record as saying that despite the club's debts, there is no financial imperative to cash in on any player. Southampton owe £27m on outstanding transfer payments, £22m of which is due in the summer, while the cost of redeveloping their training ground has risen from £15m to £30m.

Pochettino has been told that he can have the final say on transfers, in and out of the club, but the situations of Shaw and Lallana will enter his thinking as he finds his own career at a crossroads. The 42-year-old says that Southampton have completed the five-year project aimed at establishing the club in the Premier League, which was initiated by the former chairman Nicola Cortese, who hired Pochettino as a relative unknown in January 2013.

Pochettini now wants to hear evidence of the club's ambition in his talks with Krueger and the director Les Reed; essentially whether the plans for the next three or four years are sufficiently stimulating. The manager has one year to run on his Southampton contract.

Levy said in the statement released to confirm Sherwood's departure that the 18-month contract he agreed last December contained a break clause at the end of the season, which rather undermined the notion that the former midfielder was anything more than a five-month caretaker.

Sherwood endured a succession of stories while in charge that he would be replaced in the summer, as Tottenham monitored the situations of the Holland manager Louis van Gaal, Frank de Boer of Ajax and Pochettino. The club have also taken discreet soundings about the availability of Napoli's Rafael Benítez.

Van Gaal is close to an agreement with Manchester United. De Boer, who is in Indonesia with Ajax, has said that he would be open to a discussion with Levy. De Boer is under contract until 2017, which could make him more expensive to prise away.

Sherwood lost most of the big games but his Premier League record still bore scrutiny as he collected 42 points from 22 matches. "It is obviously a massive wrench to leave a club of the stature of Tottenham Hotspur, a club that is very close to my heart," he said.

Levy added: "Since appointing Tim as assistant first-team coach in 2008 and then technical co-ordinator in 2010 and head of football development in 2012, we have been supportive of him during football management changes throughout that period. We have a talented squad and exciting young players coming through. We need to build on this season, develop our potential and inspire the kind of performances that we associate with our great club."