Marin joined the Blues in a £7million move from Werder Bremen in the summer but has yet to see Premier League action this season.
The 23-year-old may look to move in order to kickstart his international career with Germany and Gladbach coach Lucien Favre could be willing to offer Marin a route out of Stamford Bridge.
"A player like Marin could be a good fit for us," said Favre, quoted in the Sunday Mirror.
"We will have to see what happens in the winter break but we have got nine games to go until then, so I don't want to say more."
Marin started his career at Gladbach and won his first Germany cap as a teenager there before moving to Bremen in 2009.