Sky go onto state that Juventus inquired about the Germany international during the January transfer window but were turned down.
However, Dortmund manager Thomas Tuchel has insisted that Gundogan may yet remain at the Bundesliga club.
“I believe it’s not the case that there isn’t a chance he’ll stay,” Tuchel was quoted as saying by SkySports.
“The importance of Ilkay in this form is undisputed, but one can imagine that the interest from other clubs is very high.”
The 25-year-old’s career began at Nuremberg before moving to Dortmund for £4m in 2011. Gundogan has six assists and three goals in 32 appearances for Dortmund this season.
The Budesliga giants have recorded 15 victories in 21 league games this season and find themselves in second place in the league.