Toprak has played for Bayer since 2011 and is vastly experienced having racked up 159 appearances in all competitions for the club.
United are reported to be looking to strengthen their defence at the end of the season and have been keeping close tabs on Toprak who still has two-years remaining on his contract.
The Red Devils are currently in the middle of an injury crisis in defence with Chris Smalling, Luke Shaw, and Cameron Borthwick-Jackson all out.
The 26-year-old defender featured for Bayer domestically and in Europe – Europa League and Champions League – as well as for Turkey.
Toprak was born in Germany but represents Turkey at international level due to having Turkish heritage.
The Bayer defender is one of many ethnic Turks born in Germany that play for Turkey and Germany at international level.