Sauer, who plays on the left, offers a different profile to Toure, given the Ivorian is naturally left-footed while the Slovakian is right-footed.
Feyenoord are said to be holding out for a fee in the region of €7m for the 20-year-old, who remains under contract in Rotterdam until 2028, giving the Eredivisie club some leverage in any negotiation.
German audiences may already have unhappy memories of Sauer following Slovakia's World Cup qualifying win over Germany last September. In a 2-0 victory for the Slovaks, Sauer repeatedly got the better of debutant Nnamdi Collins, causing enough problems down the left that the German defender was withdrawn from the game at half-time and has not featured for the national team since, effectively putting his international career on hold before it had really got going.
Hoffenheim are said to be considering other candidates for the role alongside Sauer, meaning no decision looks imminent, though the scale of the funds freed up by Toure's departure gives the Bundesliga club considerable room to manoeuvre in the market this summer.
Reinvesting a portion of a record sale into a replacement of a similar attacking profile would fit the pattern TSG have followed in recent transfer windows, developing talented young players before selling them on at a significant profit.
Toure's sale to Newcastle was itself the product of that same model, having joined Hoffenheim from Swedish club Hammarby for a fraction of the fee he eventually commanded. Sauer has followed a similarly rapid rise since breaking into Feyenoord's first team, becoming a regular for Slovakia at a young age and playing an important role in their run to Euro 2024.
A move to the Bundesliga would represent a significant step up in profile, giving him regular European football with a club that has shown it can help attacking players increase their value substantially within a relatively short space of time.