The Bundesliga outfit are understood to be keen for the 22-year-old midfielder to sign a new deal beyond 2015.
Germany international Gundogan, who joined the club from Nuremberg two years ago, enjoyed a successful run in the side last season.
He played an influential role during their run to the Champions League final and scored from the spot against Bayern Munich at Wembley in their 2-1 defeat.
"I am keen to ensure he (Ilkay) remains with Borussia Dortmund," father and agent Irfan told Kicker Sportmagazin.
"He is doing fine so it's a bit early to move to a club in England or Spain at this point in time.
"Borussia Dortmund will be coming up with an offer of a new contract soon. We will be able to oversee things much better then."
Meanwhile, BVB sporting director Michael Zorc told Westdweutche Allgermeine Zeitung newspaper: "We are keen to sign new terms with Ilkay Gundogan.
"I am able to confirm that we have held talks with his father Irfan and we feel confident he will sign."