West Ham have had a £15m for Marko Arnautović turned down by Stoke, according to Sky Sports News HQ.
Sky say the Hammers are expected to make improved offer for Arnautović, who is reported to have handed in a transfer request.
Stoke do not want to sell the player, who signed a four-year contract with them last summer.
Meanwhile, Christian Benteke is being considered by Everton as a potential signing if they are unable to land Olivier Giroud, the Mail say.
Crystal Palace’s former Liverpool striker has been linked with a move in recent weeks and the Mail say he is on Everton’s list of options.
The Merseyside club are reported to be targeting Arsenal forward Giroud, who has also been linked with West Ham.
Tottenham boss Mauricio Pochettino is interested in Estudiantes defender Juan Foyth, the Daily Mirror say.
The 19-year-old centre-back, who played for Argentina at the Under-20 World Cup earlier this year, is apparently valued at £10m.
The Mirror say his agent, former Manchester United midfielder Juan Sebastian Veron, is set to hold talks with Spurs about a potential deal.
“I would like to play in Europe, and if something comes up that convinces me and the club I will go,” the player is quoted as saying.
The Daily Star say West Ham want to sign Theo Walcott for £20m but he is keen to stay at Arsenal.
The newspaper claim Walcott has told friends he has no desire to leave the Emirates Stadium despite speculation about his future.
It comes amid reports that England international Walcott could be forced out by Thomas Lemar.
The Daily Mirror say Arsenal boss Arsene Wenger will go back with a third bid for Lemar and is convinced the France winger wants to join the Gunners.
Arsenal have reportedly had bids of £30m and £40m for Lemar turned down by Monaco.
The Sun say Wojciech Szczesny has moved closer to a move to Juventus after being left out of Arsenal’s pre-season tour.
The Polish goalkeeper is reported to have been allowed to stay behind so a transfer to Juve can be completed.
West Ham are closing in on the £8.5m signing of Senegal midfielder Badou N’Diaye from Turkish club Osmanlıspor, according to the Mirror.
And The Sun have picked up on reports in Spain claiming that Chelsea striker Diego Costa could move to Besiktas until the new year and then rejoin Atletico Madrid.
Former Atletico star Costa is reported to be keen to return to the La Liga club but they are under a transfer ban until January.
Spanish newspaper AS have claimed that Costa could therefore join Besiktas on a short-term basis.