For a list of all the completed deals, check out the transfers page.
New Manchester United manager Jose Mourinho wants to sign Italy and Juventus defender Leonardo Bonucci, 29. (Daily Star Sunday)
Striker Wayne Rooney, 30, is ready to sign a new contract so he can finish his career as a United player. (Sun on Sunday)
Mourinho is willing to trade Italian full-back Matteo Darmian, 26, for Chelsea's Serbia midfielder Nemanja Matic, 27. (Sunday People)
Watford have rejected a £25m bid from Leicester for striker Troy Deeney, 27.(Watford Observer)
Manchester City are refusing to meet Borussia Dortmund's £65m valuation of Gabon striker Pierre-Emerick Aubameyang, 27.(Manchester Evening News)
City want to sign Celta Vigo and Spain striker Nolito. The 29-year-old has a £14.1m buyout clause. (Mail on Sunday)
Pep Guardiola's side are also preparing to make a £37m offer for Real Madrid and Germany midfielder Toni Kroos, 26.(Sunday Express)
Southampton want £40m for Senegal forward Sadio Mane, 24, who is a target for Liverpool.(Sun on Sunday)
Sunderland want to bring former Manchester City striker Edin Dzeko back to the Premier League, and have offered Roma £11m for the 30-year-old.(Mail on Sunday)
Arsenal are ready to offer manager Arsene Wenger a new contract. The 66-year-old, who has one year left on his contract, will be offered a two-year extension.(Sunday Mirror)
Chelsea and Arsenal want to sign Morocco forward Sofiane Boufal, 22, from Lille, but face competition from Barcelona and Atletico Madrid.(Observer)
West Brom and Aston Villa want to sign Wales striker Hal Robson-Kanu. The 27-year-old is a free agent after leaving Reading. (Daily Star Sunday)
Juventus have identified one of a trio of Belgium players to replace 23-year-old Spain striker Alvaro Morata, who is likely to leave this summer. Everton's Romelu Lukaku, Liverpool's Christian Benteke, 25, and Marseille's Michy Batshuayi, 22, are their targets. (Gazzettaworld.com)
Liverpool's Slovakia centre-half Martin Skrtel, 31, has agreed a three-year contract with Roma. (Emanuele Giulianelli via Sunday Express)
Manchester United's Dutch defender Daley Blind, 26, is wanted by Arsenal. (Sunday People)
Leicester are preparing a £10m bid for Burnley's English centre-half Michael Keane, 23. (Mail on Sunday)
The Foxes are close to completing the signing of midfielder Nampalys Mendy, 22, after Nice accepted a revised offer of about £10m, but also want Juventus midfielder Mario Lemina, 22. (Observer)
New Everton boss Ronald Koeman has been warned off Georginio Wijnaldum, with Newcastle wanting £25m for the 25-year-old midfielder. (Sunday People)
Manchester United fear 18-year-old England striker Marcus Rashford will burn out next season if he does not get enough rest this summer. (Sun on Sunday)
Sunderland and Italy midfielder Emanuele Giaccherini, 31, would welcome the opportunity to work under Azzurri boss Antonio Conte at Chelsea, according to the player's agent. (SportItalia via Sky Sports)
The best of social media
New Everton manager Ronald Koeman tweeted a picture from Goodison Park...
Phil Neville can now manage a top-flight team after he completed his Uefa Pro Licence. The former Manchester United and Everton defender has been a coach at Old Trafford and under brother Gary Neville at Valencia. (Twitter)
Robert Lewandowski and his Poland team-mates spent their day off going for a bike ride, with the striker making sure he got a selfie. (Instagram)
Northern Ireland captain Steven Davis tweeted after he signed a new three-year deal with Southampton: "Delighted to commit my future to Southampton and hoping to build on the success we've already had."
A Leicester fan 'did a Gary Lineker' and played a round of golf in his pants. John Guest had promised to play in his underwear if the Foxes won the Premier League. Lineker has said he would present Match of the Day in his underwear if the Foxes won the title. (Leicester Mercury)
Ever wondered what England's victory over Wales would look like in Lego? Well wonder no more. (Bricksports)
Have you added the new Top Story alerts in the BBC Sport app? Simply head to the menu in the app - and don't forget you can also add score alerts your football team and more.