Hertha are said to be in the market for a winger and have been impressed by Gnabry’s performances at the Rio Olympics.
The 21-year-old has scored three goals in two games for Germany, who currently sit third in group C.
German magazine SportBild claim the Bundesliga side could look to sign Gnabry for as little as £1.7million.
His contract with the Gunners expires in June 2017, meaning he will be available on the cheap if he fails to agree a new deal.
Gnabry joined West Brom on a season-long loan last term but was recalled in January having made just one Premier League appearance.
The Germany U21 international subsequently spent much of the season playing in the Arsenal reserves and made eight appearances in the Premier League 2.
This week Germany Olympic coach Horst Hrubesch hit out at Arsene Wenger for his treatment of Gnabry and praised his recent performances in Rio.
“He did really well twice, but that doesn’t come as a surprise to me,” Hrubesch said.
“What annoys me is that people at his club have never given him enough trust during that time.
“And you can see now what an important player he can be and at what level he can play at.”