Sunderland want more than £20m for the highly-rated goalkeeper, according to reports.
Swans' beat Sunderland and stand on the brink of securing another season in the top flight.
Black Cats boss David Moyes is hopeful that the England U-21 international will remain at the Stadium of Light.
Jagielka joined Toffees from Sheffield United in the summer of 2007.
Goal-shy Teessiders' fate sealed at Stamford Bridge.
Pickford, 23, has three years left on his Sunderland contract.
Carrick, 35, is out of contract at Old Trafford this summer.
Defoe is destined to leave relegated Black Cats at the end of the season.
Josh King scores only goal as David Moyes' side become first side to drop into the Championship this season.
Joey Barton's ban, raids on Premier League clubs and Moyes' threatening behaviour are fresh scars on football's soul.
Scientists are trying to learn more about the Sun's activity to prepare for the impact of its eruptions on Earth.
Defoe has scored 14 goals and has 2 assists to his name in 32 Premier League appearances for Sunderland.
Relationship between manager and player has been noticeably strained over recent months.
However, Jose Mourinho is unwilling to disclose whether or not he intends to keep midfielder at Old Trafford.
Phil Jones, Chris Smalling and Juan Mata also remain sidelined for meeting with the sorry Black Cats.
Defoe and Lukaku have both been heavily linked with summer moves.
Rooney is struggling with pain in both his ankles, which forced him to miss the Everton clash.
The Met Office are anticipating temperatures of 23C in the south-east of England.
Black Cats boss has been widely criticised for controversial comments made to Vicki Sparks earlier last month.
The 34-year-old details the sacrifices he is willing to make to force his way into Gareth Southgate's squad.
London should be dry and warm, similar to the pleasant weather enjoyed over the past week.
Both City and Everton need to resolve their goalkeeping situations.