The Reds have been linked with the Swiss World Cup star for the past few months, but speculation had suggested that there interest had cooled following the arrival of Lazar Markovic from Benfica.
But now it appears that the Merseysiders are indeed still chasing the 22-year-old after making a concrete offer.
Shaqiri – who helped his nation out of their group in Brazil – is expected to leave Bayern after two unproductive seasons before the new campaign kicks off, despite being urged to stay at the Allianz Arena by members of the Bavarians’ hierarchy.
Juventus and Roma have also been linked with the star, but the lure of life in the Premier League and greater wages may sway him.
Reports earlier in the week suggested that he was ready to stay in Germany, however these have been deemed to be wide of the mark.