Zelalem is currently on loan at Dutch side VVV-Venlo after struggling to break into Arsenal's first team.
The 20-year-old had been linked with a move to Borussia Dortmund but will hope to gain regular senior level experience at Venlo.
Fans reflect on Arsenal's woeful defeat to Chelsea
Sat, February 4, 2017
Express Sport brings you the best tweets as Arsenal fans reflect in their woeful defeat to Chelsea on Saturday
1 of 10
Arsenal fans reflect in their woeful defeat to Chelsea on Saturday
While Loftus-Cheek was wanted by a number of clubs in January but Chelsea boss Antonio Conte was determined to keep hold of the England under-21s international.
But he has played just 14 minutes of Premier League football this season and is understood to be growing frustrated at his lack of opportunities.
Arsenal midfielder Gedion Zelalem
And according to German newspaper Bild, Gladbach are hoping to take advantage of the uncertainty surrounding Zelalem and Loftus-Cheek.
It is claimed both players are on their summer wishlist and sporting director Max Eberl is keen to push ahead.
Get Quotes on Home Insurance
Chelsea’s Ruben Loftus-Cheek
He is quoted as saying: "The English market is very interEsting for us.
“Of course not the top stars of the Premier League, but the squad [players].
“Many youth national players go there, but then face a barrier.”