Antonio Ruddier, Alvaro Morata, Tiemoue Bakayoko and Willy Caballero have all joined the reigning Premier League champions this summer.
But Antonio Conte has been vocal about his displeasure with the size of his Chelsea squad and his desperate to add more bodies.
Chelsea missed out on Romelu Lukaku to rivals Manchester United while Jose Mourinho's side also nabbed Nemanja Matic from Stamford Bridge.
But the Mirror claim Roman Abramovich is ready to back Conte in the remaining weeks of the transfer window.
The Blues have been linked with a move for Arsenal star Oxlade-Chamberlain recently but it is said Chelsea are now ready to offer £35m for the England international.
The 23-year-old's future at Arsenal is uncertain as he seeks assurances over his role with the Gunners with a number of Premier League clubs reportedly interested in his signature.
Oxlade-Chamberlain also has just 12 months on his contract and it is suggested he doesn't want to sign a new deal at the Emirates.
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