The 19-year-old joined the Royal Blues in February last year but limited first team opportunities have thrown his future at Veltins-Arena in doubt.
He made two Bundesliga appearances last season in addition to a 90 minute outing in a 2-0 triumph over Nice in the Europa League.
His promising debut earned him a place in Ghana's squad for the Africa Cup of Nations early this year where he featured twice.
Goal sources say while Tekpetey is keen on pursuing a move away for regular action, Schalke want the youngster to remain in Gelsenkirchen in the new season to fight for his place.
Hamburg have shown interest in the attacker, whom they want to purchase in an outright deal, whereas Schalke are only likely to consider a loan option should they decide to send out the player this season.
Bundesliga 2 side VfL Bochum are another possible destination, as they are keen on signing the Ghana international on loan.
After featuring in a 1-0 friendly win over Paderborn on Saturday, Tekpetey travelled with Schalke to China as preseason intensifies.
The future of the youngster would likely be decided upon the team’s return from Asia.