The Sunday Mirror say Arsenal believe they could be favourites to sign Adrien Rabiot.
The France midfielder previously played under Arsenal boss Unai Emery at Paris St-Germain, where his contract expires this summer.
Rabiot been linked with a number of Premier League clubs, including Tottenham, but it is claimed that the Gunners are in a strong position to snap him up on a free transfer.
Meanwhile, Arsenal midfielder Emile Smith Rowe, who has been loaned to RB Leipzig, will be unable to train for at least three weeks because of a groin injury, the Independent on Sunday reports.
The Mail on Sunday again suggest that former Arsenal winger Marc Overmars is in the line to return to the club as director of football.
Manchester City have again been linked with Crystal Palace defender Aaron Wan-Bissaka.
The England Under-21 international was linked with the Premier League champions ahead of the recent transfer window.
And The Sun on Sunday claim City boss Pep Guardiola wants to sign Wan-Bissaka and Leicester left-back Ben Chilwell when the window reopens.
Tottenham are preparing a move for Bournemouth midfielder David Brooks this summer, the Sunday Mirror say.
The newspaper reports that Manchester United want the Wales international but that Spurs plan to table a £50m bid in order to get him.
Spurs were linked with Brooks prior to his move from Sheffield United to Bournemouth, where he has been outstanding this season.
The Sunday Mirror say questions have been asked at Spurs as to why they did not pursue a deal to sign Brooks and that the club will do so at the end of the season.
The Sunday Express claim Chelsea could look to install Spurs boss Mauricio Pochettino as their manager this summer.
Bayern Munich are planning a £45m bid for Chelsea’s Callum Hudson-Odoi, according to The Sun on Sunday.
And West Ham did not sign Michy Batshuayi or Maxi Gomez because they were unwilling to pay either strikers’ £80,000-a-week wages, the Sunday Express say.