The Whites suffered relegation from the Premier League last season and a number of players are keen to leave the Elland Road outfit this summer.
Wober is a player Leeds would have liked to have kept, but he is not keen on playing in the Championship and is heading to Germany.
He has agreed on personal terms with the German club and is now set to undergo his medical within the next 48 hours.
Sccording to Sky Deutschland, Gladbach are set to confirm the signing of Wober on Monday.
It has also been claimed the German side will pay €500,000 to the Championship side to loan the defender.
He will join Die Fohlen on a season-long loan, but it is not yet clear whether there will be an option to buy in the agreement.
Wober, 25, joined the Elland Road outfit in January and played in 16 Premier League matches for the Yorkshire-based side.
