The England international hopes to play at least 75 minutes against Roberto Di Matteo's second-string as he looks to rebuild his match fitness.
Wilshere has spent almost 17 months on the sidelines with various knee, ankle and foot injuries, but the Arsenal midfielder has slowly stepped up his recovery with a series of managed appearances for the Gunners' under-21 side.
The England international completed 63 minutes against West Bromwich Albion at the beginning of the month, before managing 74 minutes against Reading.
And Wilshere will hope to continue to ramp up his playing time tonight in what will be his sternest test yet. The behind-closed-doors friendly is scheduled to take place this afternoon at Arsenal's training base in London Colney, but Wilshere is not the only Gunners star expected to feature against the Blues.
Bacary Sagna and Emmanuel Frimpong are both likely to start for the Gunners as they slowly work their way back to full fitness.
According to the Daily Mail, both are nearing a first-team return, and should feature for Arsene Wenger's front side before Wilshere.
The 20-year-old will not be rushed back by Wenger, and Arsenal are believed to have pencilled in their match with Reading on October 30 as the target date for Wilshere's return.
In order for that to happen, the Arsenal youngster will have to get through today's game, and another 90-minute appearance for the under-21's against Everton next week.
Sagna and Frimpong should be in contention sooner, and could feature for Arsenal in this weekend's squad to face Norwich on Saturday evening, assuming they emerge unscathed from today's fixture with Chelsea.