The central midfielder???s current deal with the Bundesliga side expires at the end of next season and his refusal to sign a fresh contract increases the likelihood he will be sold this summer.
Gundogan has been strongly linked with a move to Manchester United and the Old Trafford outfit are close to agreeing a ??21.5m deal to sign him, according to reports.
The 24-year-old, who has made nine appearances for Germany, started his career with Bochum, before moving to Nuremberg.
Dortmund signed him in May 2011, and he helped them reach the 2012-13 Champions League final. He scored a penalty in the final against Bayern at Wembley, although Dortmund lost the match 2-1.
He was sidelined for over a year with a mystery back problem which baffled doctors and forced him to miss Germany???s World Cup triumph in Brazil.
Manchester United manager Louis van Gaal stated in February that he wanted to sign a creative midfielder in the summer and Gundogan, who is technically accomplished and a fine passer – as well as a tenacious tackler – certainly fits the bill.
He was signed by coach Jurgen Klopp – who will leave Dortmund at the end of the season – to replace Real Madrid-bound??Nuri Sahin, and he initially struggled to make an impact.
But he made the breakthrough in the 2012-13 season, helping Dortmund to their first league and cup double, and the final of the Champions League the following season.
He has scored 15 goals in 123 appearances in the Bundesliga, and one goal – that penalty at Wembley – in 20 Champions League appearances.??