Wigan boss Chris Hutchings confirmed Everton's recent interest, but insisted no deal had been agreed.
Sunderland had sprung a surprise by beating Everton thus relieving some of their relegation concerns.
The centre-back has had a chequered career at City since joining them from Everton in 2000.
His final two games as Everton manager will be against West Ham United and Chelsea.
"Everton officials will start the search for a replacement manager immediately, " added the Everton statement.
Blackpool booked an FA Cup fifth-round tie at Everton after comfortably beating Sheffield Wednesday.
Premier League midfield duo Steven Pienaar of Everton and Fulham's Kagiso Dikgacoi were both selected.
Denilson then fired over and Phil Neville magnificently blocked Thomas Vermaelen's shot as Everton stood firm.
Owen has also recently been linked with a move to Aston Villa and Everton.
Everton's lead lasted only two minutes when a moment of defensive slackness gifted Blackburn an equaliser.
But in 11 seasons at Everton, he finished in the top eight on nine occasions.
Liverpool and Everton fans have teamed up to help regenerate deprived areas in north Liverpool.
Chelsea will still have to play a somewhat resurgent Aston Villa side and sixth-place Everton.
"Reading have beaten West Brom and Everton, so it won't be easy, " he added.
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But the Everton supporter took pride at the performance of his players against the European champions.
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The only Premier League team Wigan eliminated was Everton, beaten 3-0 in the quarterfinal.
Aston Villa go to West Ham waiting to pounce if Everton were to slip up.
Everton confirmed the acquisition of the 30-year--old French international on the club's Web site.
Everton's David Moyes said team selections should not fall under the Premier League's jurisdiction.
He becomes Blues' second experienced addition of the summer, following Everton midfielder Lee Carsley.
Lescott played for Everton on Saturday as they were thrashed 6-1 by Arsenal at Goodison Park.
Everton are 13th in the table and only three points above the relegation zone.
Everton will play Reading in the last 16 at Goodison Park on Tuesday, 1 March.
But Everton stunned Stamford Bridge by equalising at the death through a curling Leighton Baines free-kick.
Arsenal still has Swansea (away this coming weekend) and Everton and Manchester United at home.
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But Olomouc would be made to regret their profligacy and Everton soon took control of proceedings.
The summer deadline passed without the former Everton player getting a move from the Banks's Stadium.
David Moyes' side entertain Chilean side CD Everton on Wednesday, 4 August in a pre-season friendly.
Everton are weighing up a move for Ajax's highly rated Belgium international defender Jan Vertonghen.
The opening exchanges were tight, but it was Everton who created the better opportunities.
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