The former Welsh international goalkeeper was brought in from Everton for the last 12 games of Stoke's vain battle to avoid the drop. He was released on a free transfer from Goodison Park in March.
Stoke's caretaker manager, Alan Durban, confirmed his spell in charge was over after Sunday's 5-2 defeat by Manchester City that sealed their fate. Southall has already been in discussions with the board at the Britannia stadium.
"I want to stay at Stoke and I want to play for the club," Southall said. "I would like the job as manager, but there would have to be changes. But any time a club goes down there is always a change of personnel."
Southall was signed as a player-coach by Chris Kamara before the former Bradford City manager left after just 14 matches in charges without having achieved a victory.
Bradford City are trying to sign the full-back Chris Short, soon to be out of contract at from Sheffield United, on a free transfer.
West Ham have agreed to sign the French international midfielder Marc Keller from the German club Karlsruhe on a free transfer under the Bosman ruling. The 30-year-old, who hopes to be included in the French squad for the World Cup, has signed a four-year contract due to start in July.
Alex Ferguson has watched the Cameroon international, Marc Vivien Foe of Lens. The Manchester United manager saw him in action in Saturday's French Cup final in Paris.
Foe, who can play midfield or defence, was on the losing side as Lens went down 2-1 to Paris St-Germain.
Sky Sports will broadcast Ipswich against Charlton in the first leg of the First Division play-off semi-finals on Sunday at 1pm. At 4pm, Sky will simultaneously screen Everton's vital Premiership home game with Coventry and Chelsea against Bolton from Stamford Bridge on different channels.Reuse content