The 19-year-old right-back, who can also slot into central defence or push forward on the right wing, has enjoyed a breakthrough campaign in the 2. Bundesliga with 22 league appearances, notching one goal and one assist.
A product of Bayer Leverkusen's academy, Bulut joined Schalke determined to find first-team football - and has done just that.
His rapid development has seen his market value skyrocket from 250,000 euros to 5 million euros over the course of the season.
Despite Schalke's hopes of keeping the Germany U19 international, a summer move looks increasingly likely. Bulut's contract includes a 6-million-euro release clause, a figure several suitors appear ready to meet or exceed.
Bundesliga outfits Stuttgart and Freiburg are both monitoring the situation closely. Freiburg, in particular, are understood to be willing to offer up to 8 million euros should they secure Champions League qualification.
Interest extends beyond Germany as well. Italian side Atalanta were linked with Bulut in January, and Austrian champions RB Salzburg remain keen.
Harry Kane has expressed his delight at securing his first major trophy after Bayern Munich were crowned Bundesliga champions, with the England captain now setting his sights on further silverware.
Bayern Munich were officially crowned Bundesliga champions for the 33rd time on Sunday, following Bayer Leverkusen's 2-2 draw against SC Freiburg.
England captain Harry Kane lifted the first major trophy of his career on Sunday as Bayern Munich were officially crowned Bundesliga champions for a record-extending 33rd time.
RB Leipzig put in one of their best performances of the season to deny Bayern Munich the chance of securing the Bundesliga title on Saturday.
