Mitroglou scored three goals for Greece in their World Cup play-off win against Romania.
The Daily Mirror reports that Liverpool head of recruitment Dave Fallows and chief scout Barry Hunter were in Romania to watch the striker in action.
The pair also watched the first eg of the tie in Greece.
Liverpool scouts have reportedly watched the striker’s last six matches.
Liverpool boss Brendan Rodgers is keen to bring in cover for star duo Luis Suarez and Daniel Sturridge.
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The start of the 2017-18 Premier League season is just around the corner and is shaping up to be one of the most competitive yet.
As always it is the so called “big clubs” that have splashed the most cash in the transfer window so far this summer. Manchester United or City? Arsenal or Tottenham? Who are the winners and losers of the transfer window so far?