West Ham and Crystal Palace want Everton midfielder James McCarthy, according to the Mail on Sunday.
Newcastle are also said to be keen to sign the Republic of Ireland international, who has been tipped to leave Goodison Park this summer.
Everton are reportedly willing to sell McCarthy, 26, for £20m.
Meanwhile, Chelsea have again been linked with Tottenham’s England defender Kyle Walker.
The Sunday Mirror say Spurs are willing to sell Walker, 26, for £40m and that this “will spark a bidding war” between Chelsea and Manchester City.
The Sunday Express say Manchester United could snap up Walker in a swap deal involving left-back Luke Shaw.
The Sunday Express also claim Chelsea are struggling to hold on to Antonio Conte amid interest from Inter Milan.
It follows recent reports that Inter are keen to appoint the former Italy and Juventus boss, who has led Chelsea to the title this season.
Chelsea midfielder Nemanja Matic has again been linked with a possible move to Chelsea, this time by the Sun on Sunday.
United’s former Chelsea manager Jose Mourinho is planning a £35m bid for the Serbian, it is claimed.
Chelsea are interested in signing 20-year-old Russian midfielder Alexsandr Golovin from CSKA Moscow, according to the Mail on Sunday.
The Sunday Times report that Arsene Wenger expects to stay on as Arsenal manager and believes a new contract for him will be announced after the FA Cup final against Chelsea next Saturday
And The Sun on Sunday say Tottenham will offer £12m for Fulham’s teenage left-back Ryan Sessegnon.