Chelsea, who will be seeking around £40mn, have been in regular dialogue with the Italian champions over their Brazilian defender Alex Sandro, with Matic's future expected also to be up for discussion.
Both players have been heavily linked with exits this summer, with Oxlade-Chamberlain having just 12 months remaining on his Arsenal contract.
His non-inclusion in the tour party is a clear sign by manager Antonio Conte that he expects the Serb midfielder to move on, with Chelsea set to complete the £39.7m signing of Monaco's Tiemoue Bakayoko last night.
Matic reported for training with the rest of the Blues squad but spent much of his time alone.
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Given the fact that Serbian global Nemanja Matic also holds a Slovak citizenship, it would exempt him from occupying a non-EU spot in the team both of which have been taken by Douglas Costa and Rodrigo Bentancour.
The Brazilian is one of Antonio Conte's priority targets but the Serie A champions are demanding a £65 million transfer fee.
Jose Mourinho is willing to wait on Chelsea to make a decision over Nemanja Matic before he instructs his board who else to move for this summer.
However, he hasn't yet reached his full potential, while signing Matic would give Arsenal that powerful presence in midfield that they've been lacking for years.
The Gunners are keen for the 23-year-old to stay but speculation suggests The Ox is ready for a new challenge and it seems Arsene Wenger is now trying to use him as bait to get his hands on Matic.