The Reds opened negotiations with the Bundesliga club but the midfielder prefers the prospect of a move to Catalunya.
Having landed RB Leipzig Naby Keita, 22, Jurgen Klopp is determined to overhaul his midfield. The process began with the signing of Alex Oxlade-Chamberlain, 24, with the German manager looking to add his fellow countryman to his squad.
Goretzka is much in demand with rumours of a deal to Bayern Munich emerging last year but coming to nought. Now under the control of Jupp Heynckes, the Bavarians remain keen to land the German international.
With his contract expiring next summer, Goretzka can talk to foreign clubs from January. As well as Liverpool, both Arsenal and Chelsea are expected to renew their previous interest in the midfielder.
Schalke, while not giving up hope of the youngster signing a new deal, face a choice of whether or not to cash in on Goretzka in the next transfer window.
Having signed him for €3m from Bochum in 2013, Die Königsblauen are not entitled to any compensation if Goretzka leaves on a free transfer next summer.
For Barcelona, already contemplating a €100m+ bid for Philippe Coutinho, 25, the prospect of acquiring one of Europe’s hottest properties for nothing may be too much to resist.