Oxlade-Chamberlain had a fantastic season for Arsenal past year, playing in a variety of positions, including right wing, central midfield, and even as a right wing back.
Initial rumors put his price at £25m, but that seemed far too low, even with just one year left on his contract (which apparently Arsenal are more than happy to run down because silly reasons).
The Daily Star has revealed that the Blues have raised their bid after they initially offered £25 million for the 23-year-old.
Antonio Conte is desperate for reinforcements, and has grown increasingly frustrated at the lack of transfer activity at the club, and sees Oxlade-Chamberlain as a player who can give Chelsea a really good option at wing-back.
Oxlade-Chamberlain is one of the Italian's top targets and he is now poised to test Arsenal's resolve to hang onto him.
However, Chelsea are said to have made a move for the England global while there is also interest from Liverpool.
Speaking ahead of Arsenal's first game of the new season against Leicester City, Wenger said of Oxlade-Chamberlain: 'I think in his career he had some bad moments because he had some small injuries.
Arsene Wenger has insisted he wants Oxlade-Chamberlain to stay, but if Arsenal can agree a new contract with the player or not remains to be seen. Previous year he was much more stable. He is on the way up and he will continue to move up because that potential is there.
As per the Daily Star, Conte is a huge admirer of Oxlade-Chamberlain, and has highlighted him to the Chelsea board as a player he would like them to sign before the end of the transfer window.