The 19-year-old was recently recalled to London Stadium after joining the Bundesliga club on loan last summer.
Despite making just four appearances for Gladbach, the versatile defender is held in high esteem and manager Dieter Hecking believes staying in Germany will be the best way to cultivate Oxford's talent.
Hecking said: "The ball is now with West Ham and Reece made a clear statement saying he would like to continue playing football in Gladbach and I personally believe that would be the best for his development."
Oxford is expected to meet with the Hammers on Tuesday to discuss his future. He is currently tied to the club until 2021 after signing a long-term extension in 2016.