Goal understands the Potters have an option to sign Wollscheid, a 25-year-old centre-back who joined Mainz on loan last summer, for £3 million should he impress Mark Hughes between now and May.
Wollscheid joined Leverkusen in 2012 from Nurnberg and has made over 50 appearances for the club, but found himself surplus to requirements this season and has fared little better at Mainz, making just five appearances.
"Philipp is a player we've been aware of and have been tracking for some time and he will add to the competition for places in the centre of our defence," Hughes told Stoke's official website.
"He's got presence, technically he is good, he has played at a high level and he has gone for big money in the past and to get a German international at relatively young age is a good deal for the club.
"He's genuinely excited about the prospect of playing in the Premier League and is confident of making a big impression as a Stoke player."Wollscheid becomes Hughes' first signing of the January transfer window and bolster Stoke's central defensive options alongside the likes of Ryan Shawcross, Marc Muniesa, Marc Wilson and Robert Huth.