The versatile star has just one year remaining on his current contract at the Emirates and is still no nearer to agreeing terms over an extension.
And now the Daily Mail claim the Premier League champions have stepped up their in Oxlade-Chamberlain, launching an opening bid of £25m.
With Oxlade-Chamberlain allowed to discuss terms with any club interested in him, in January, ahead of a move next summer, Arsenal may be forced into selling the England global this summer in order to avoid losing him for nothing.
Chelsea clearly need to make swift progress to embolden their squad ahead of the new season, and Chamberlain appears to be a good place to start.
Chelsea have submitted a new bid of £35million for Arsenal playmaker Alex Oxlade-Chamberlain, according to a report.
The blues manager Antonio Conte, who earlier this week was reassured that at least three more new players would arrive at Stamford Bridge before the transfer window closes, is understood to be desperate to signthe Arsenal midfielder.
The north London side have also signed Alexandre Lacazette in a club-record £52m deal from Ligue 1 side Lyon.
Chamberlain will fit in well at wing-back where he has impressed so far with Arsenal since Arsene Wenger switched to three-man defence system.