The defender, who spent last season on loan with the Bundesliga side, was the subject of a £14.5million bid to bring him back to Germany on a permanent basis.
However, Chelsea have rejected the offer with Antonio Conte mindful that John Terry is approaching the end of his career.
Terry, who lifted the Premier League title just a year ago, struggled for consistency under both Jose Mourinho and Guus Hiddink last season.
Gary Cahill and Kurt Zouma are thought to be the Blues’ centre-back pairing of the future, with the latter recently returning to training after five months out with a knee injury.
Christensen made his Blues bow under Mourinho in a 2-1 victory over Shrewsbury Town in 2014.
He made just one league appearance that season – in a 3-1 win over Sunderland – before leaving on loan last summer.
The 20-year-old impressed for Monchengladbach and will again spend this season with the German side, having signed a two-year loan deal.
However, it looks like Conte views him as a key part of his plans for the future and a permanent move away from Stamford Bridge is out of the question.