German publication Express reports that Pep Guardiola has lined up the 19-year-old as a potential solution to City's problems in the full-back positions.
City failed to make additions in those areas in the summer and have rotated between veterans Pablo Zabaleta, Bacary Sagna, Gael Clichy and Aleksandar Kolarov this term.
All have struggled to make the right-back and left-back spots their own, however, and Guardiola is likely to seek reinforcements as soon as possible.
Henrichs, who can operate on either side of the defence and also in midfield, made his Leverkusen debut at age 18 has already been capped by the senior Germany team.
"There are many clubs that are interested in Benjamin," his representative Ali Bulut told Express. "But the boy is only 19 years old, last year he still played in the youth team.
"He is supposed to grow up first. In Leverkusen, he is in the best position at the moment."
City's only January signing so far is Brazilian forward Gabriel Jesus, whose arrival this month from Palmeiras had been prepared in advance by the club.
Goal understands Guardiola and Txiki Begiristain are exploring the possibility of making further additions but the club's official line has been that more business is unlikely.
If that is the case, City will almost certainly look to bolster their squad in the summer, with a number of key players now over 30 years of age.