Wilshere has been out for more than 15 months with persistent ankle and knee injuries but is on the verge of a first-team return.
Gunners boss Arsene Wenger has arranged the fixture against Chelsea to aid Wilshere's recovery, according to The Sun.
The 20-year-old has played twice in recent weeks for the Under-21 side, completing just over an hour on both occasions.
Gunners boss Arsene Wenger is close to welcoming back a trio of players who have been on the treatment table with long-term injury problems.
Wenger is thought to be targeting Arsenal's Capital One Cup tie against Reading on Tuesday, October 30 as a chance to hand Wilshere his first first-team appearance of the season.