Cornelius arrived at Cardiff after a £7.5m move in the summer, but has made just 11 appearances, failing to score a single goal, and is expected to rejoin his former club this month.
A Copenhagen statement on twitter read: "The club is close to sign a deal with @CardiffCityFC striker Andreas Cornelius. More to come in the following days."
The recent arrival of Kenwyne Jones has pushed Cornelius further down the pecking order and new manager Ole Gunnar Solskjaer has decided to recoup some of the money that Cardiff spent on the 20-year-old.
Reports suggest that Cornelius will head back to Denmark in a deal worth around £3m, a hefty loss on a player who also attracted interest from Middlesbrough and CSKA Moscow.
Fellow forward Joe Mason could also be heading away from Cardiff as he has been linked with a loan back to Bolton.