The 23-year-old has been an outcast at Anfield following Jurgen Klopp's arrival at the club and last played a competitive game for the Reds in May 2015.
The Serbian allegedly refused to leave the club last summer, however, and still has 18 months remaining on a contract that sees him take home around £35,000 a week in wages.
Last week it was reported that Russian Premier League leaders Lokomotiv Moscow had made enquiries for the winger, and yesterday Premier League strugglers Swansea City were said to have also entered the race.
According to the Daily Mail, Markovic now has a third potential suitor, with Bundesliga side Wolfsburg "trying to persuade" the player to join them.
The newspaper adds that Klopp's side are weighing up the offers for Markovic and are hopeful of offloading him on a permanent deal before tonight's deadline.