The former Chelsea winger has been put on the Bundesliga club's transfer list and did not feature for BVB in Monday's pre-season friendly win over Liverpool in the USA, as he has been released by the club's pre-season tour squad to negotiate with other clubs.
And according to the Daily Mail, Dortmund has offered the 27-year-old to Everton and Crystal Palace this summer, while newly-promoted Fulham hold a significant interest in bringing Schurrle back to west London. The winger is also being targeted by Serie A side Lazio.
The offering of Schurrle to Crystal Palace holds some significance as Dortmund are interested in signing Eagles' winger Wilfried Zaha this summer. The German winger could be used as part of a potential deal to prize Zaha away from Selhurst Park, with Palace proving to be tough negotiators, valuing the 25-year-old Ivorian at £60m.
Everton, meanwhile, could be on the look-out for a wide player, should Ademola Lookman leave the club. The 20-year-old, who spent the second half of the 2017/18 season at Dortmund's Bundesliga rivals RB Leipzig, has been subject to a permanent offer from the club and could leave Goodison Park over the summer.
Fulham are equally on the look out for a winger, as the Cottagers have also been strongly linked to Bordeaux winger Malcolm over the past few weeks. Schurrle would be deemed as the cheaper option, while his links to west London could favour the newly-promoted side.
Since leaving Chelsea in 2015, Schurrle has had a mixed return to the Bundesliga. He joined VfL Wolfsburg for a £22m fee and scored ten league goals in just under a season and a half for Die Wolfe.
The 27-year-old then joined Dortmund two seasons ago for around £25m, but has only accumulated 33 Bundesliga appearances over those two campaigns at Signal Iduna Park.
Schurrle has, however, been prominent on the international stage, scoring 22 goals in 53 appearances for the German national side, but did not receive a call-up to Joachim Low's side for the 2018 World Cup over in Russia.