Wolf joined Gladbach from RB Leipzing on a permanent deal for £8million this summer following a successful loan spell, but has struggled to secure a permanent place in the German club’s starting XI.
Manager Adi Hutter is prepared to let Wolf leave the club on loan in January, but his availability has put many clubs in Europe on alert.
Celtic have been monitoring the attacking midfielder, who plays predominantly in a No 10 role, for some time, but German news outlet Bild suggest that Turkish club Trabzonspor and Rapid Vienna in his homeland would also be keen to sign him.
Wolf played against Celtic in 2018 when he was at RB Salzburg. Known as a goalscoring midfielder, he has been capped 15 times by Austria’s Under-21s, with eight goals to his name.