The Sunday Mirror says the 20-year-old Arsenal midfielder has been out for 14 months with knee and ankle injuries.
But he is now back in full training - and could play against West Brom reserves on Monday, October 1.
Manager Arsene Wenger is wary of rushing back his England star prematurely, but has warned Wilshere will be even better when he returns.
But he has been highly impressed with the progress Wilshere has made in his rehabilitation.
Wilshere has benefitted from voluntary DOUBLE sessions in the last month as he battles for his return.
He has been monitored by the club medical team, but Wilshere has shown total dedication in his push to be fit as soon as possible.