The German side have confirmed that the 25-year-old will not be renewing his contract when it expires this summer.
Monchengladbach have also confirmed that the Norwegian international is set for a move to England.
West Ham are one of the clubs who have been strongly linked with a move for the midfielder.
Havard Nordtveit has opted not to extend his contract and will move to England in the summer. #fohlenelf pic.twitter.com/nE5DMNL6an
— Borussia (@borussia_en) March 13, 2016