The forward reportedly has a get-out clause in his contract which allows him to move at the end of the season if any club meets a fee of €35million (£28.5m).
Leverkusen, who sit second in the Bundesliga, could therefore try to sell Schurrle in the winter transfer window to gain a higher price.
European champions Chelsea could take advantage and are understood to have tried to sign the forward in summer 2012 while the struggles of Fernando Torres could inspire a new bid
But Schurrle's father, Joachim, has ruled out any move before the end of the campaign, as he told Express newspaper: "We have plenty of time left until the next summer.
"Until next summer, there is no reason to move. Moving clubs before the summer is not an issue. Andre very much likes being at Bayer Leverkusen.
"It's a successful team and the team plays really good football, too. We all simply have to wait and see."