Christensen, 20, has impressed during a two-year loan stint with the German club and was named their player of the year for 2015-16 ahead of Granit Xhaka.
Gladbach had hoped to sign him permanently at the end of the current campaign but appear to have conceded defeat on that front on the same day it was announced that star midfielder Mahmoud Dahoud would join Borussia Dortmund.
"He must go back to Chelsea," sporting director Max Eberl said, according to Kicker. "Those are the two players [Dahoud and Christensen] that we have to replace in the summer.
"There are no others. And we don't want any others [to leave us]."
Chelsea's search for defensive reinforcements has been well documented, with Cesar Azpilicueta, David Luiz and Gary Cahill playing the bulk of the games in Antonio Conte's three-man defence this season.
John Terry is out of contract in the summer and Kurt Zouma is yet to re-establish himself in the first team after a serious knee injury, leaving Conte short of depth.
Nathan Ake was recalled from his loan with Bournemouth in January to provide extra backup and could be joined by another academy graduate in Christensen in battling for a place in the starting lineup in 2017-18.