The 33-year-old made the switch to the Ricoh Arena on a 35-day agreement last week after failing to get into the Villa first team.
After making his debut in the Sky Blues' goalless draw against Rochdale on Tuesday, Cole has opened up about his desire to stay at the club beyond his loan.
"I enjoyed it, I knew it would be 50 to 60 minutes but it was nice to get out there," Sky Sports News quotes Cole as saying.
"The plan was to come in and work hard and I literally trained once with half the team, but I'm really enjoying my time here early on. I'm impressed, it's nice to play for points and I want to be here for the long term."
Cole spent seven years at Chelsea before having spells at Liverpool, West Ham United and Villa.