Markovic spent last season on loan at Fenerbahce, but has returned to Merseyside for pre-season.
Chelsea's Filipe Luis in action with Liverpool's Lazar Markovic
Markovic returned to the club this summer following a season-long loan spell at Fenerbahce and has played in both of Liverpool's pre-season games so far.
However, the Reds are reportedly sourcing a move for the Serbian who signed from Benfica in 2014 for £20 million, with the lack of European football meaning the squad needs trimming in the eyes of manager Jurgen Klopp, with Goal's report saying he would be staying put if the Reds had European commitments.
Liverpool's Lazar Markovic
There haven't been any formal talks about a possible transfer just yet but there has been interest from clubs in Spain and Italy as well Sporting Lisbon in Portugal.
They also state that they would not discount loan offers if there was a 'sizeable' fee attached to the offer.
It's clear that Markovic is rated highly by Klopp otherwise he wouldn't have tried to bring the player back from his loan spell in Turkey midway through last season - therefore it would be a shame if they had to the let the 22-year-old go on a permanent basis.
Liverpool manager Juergen Klopp
Liverpool have already sold one natural wide player in Jordon Ibe to Bournemouth for £15 million, and given that a lack of pace in wide areas was a problem last season, one does wonder if letting Markovic go would be entirely wise.
The Reds have added pace in Sadio Mane but it feels as though the side could do with another player from deeper role than the forwards who can be quick enough, though at his age Markovic does need game time. It will be interesting to see where he ends up at the start of the season, and if it's away from Anfield, whether it's on a permanent basis or not.
Fenerbahce's Lazar Markovic in action with Celtic's Kieran Tierney and Stefan Johansen