The Reds are currently in their first transfer window with German manager Jurgen Klopp at the helm, with Brendan Rodgers having been in charge during a big-spending summer.
But despite the vast levels of cash sent out of Anfield for star names, the current Kop chief is noticeably short in terms of pace in his side, especially from wide.
Aside from Jordon Ibe, Klopp lacks any sort of direct threat from either flank, and reports claim that he’s keen to address this with Kostic.
The 23-year-old is a player the Merseyside manager knows will from his time in the Bundesliga with Dortmund, and the club likely to have been impressed by his chance creation rate this term – only seven players have created more chances in BuLi action.
A Serbia international, Kostic could join compatriots Marko Grujic and Lazar Markovic at Liverpool – the former is close to joining from Red Star Belgrade, while the latter is on loan at Fenerbahce.