The 26-year-old has racked up 34 goal involvements in 61 Bundesliga appearances, a return widely regarded as too strong for the second tier, and VfL Wolfsburg are prepared to let him leave before next Tuesday's deadline — via a loan if necessary — despite his contract running until 2029.
According to L'Équipe, newly promoted Schalke are among the clubs showing concrete interest in the Algeria international, alongside Olympique Marseille and a number of other French and Italian clubs.
Amoura is currently working his way back from a thigh injury that will keep him out of Wolfsburg's second-tier opener against Kaiserslautern, but he has made no secret of his desire to remain playing at the highest level available to him following relegation.
Wolfsburg signed Amoura permanently from Royale Union Saint-Gilloise last year for a fee in the region of €18million, after an initial loan spell, and his stock rose sharply following an outstanding debut Bundesliga campaign that yielded ten goals and 12 assists.
His form dipped last season as Wolfsburg slid towards the drop, managing eight goals and four assists before losing his starting place altogether in the closing weeks, but he remains highly regarded across the German top flight and beyond.
Schalke exploring their options is a natural duty for sporting director Frank Baumann's recruitment department, though funding Amoura's wages — believed to be close to €5million a season — would almost certainly require financial assistance from Wolfsburg to make any loan deal workable.
On present evidence, such an arrangement coming together before the deadline looks unlikely, though Schalke's interest underlines the scale of Amoura's continued appeal even after relegation.
Amoura's situation is complicated further by conduct issues that surfaced over the course of last season, with several reports in Germany pointing to friction within the Wolfsburg dressing room contributing to his eventual loss of form and starting spot.
Even so, few clubs would dispute his talent, and his combination of pace and directness continues to make him one of the more sought-after forwards likely to change clubs in the closing days of the German transfer window.