Toure is based in London and it's understood his agents recently contacted Orient to see if he could use their Chigwell training ground, says the Daily Mail.
The midfielder has not played in English football since leaving City at the end of the 2017/18 season.
From there he moved to Olympiakos in Greece and most recently to the Chinese Super League with QD Huanghai.
He told Orient's website: "The manager and the staff were fantastic in allowing me to come train with the lads. It's a huge opportunity. I'm very happy. The welcome was fantastic.
"I just want to enjoy it until the last minute. Football, for me, is everything. I've been out of football for the last three months with the lockdown and I was thinking I missed something. It's difficult. I feel like I'm at home. I want to train and do my best, and maybe we'll see."