The 27-year-old is out of contract at the end of the season but is said to have rejected the chance to move away by opting instead to run down his deal before weighing up his options next summer.
German newspaper Bild claim that Rangers, West Brom, Basel and Copenhagen all tried to sign the former Germany Under-21 international towards the end of the transfer window, but he decided to stay in the Bundesliga.
Selke has made just two starts and four substitute appearances for Hertha so far this season, scoring one goal.
His former clubs include Werder Bremen and RB Leipzig. In total he has made 194 appearances in the German top flight, netting 34 times.
Former Germany striker Klaus Fischer once described Selke as being a "young Miroslav Klose", comparing his stature and strength in the air with that of Germany's all-time record goalscorer.