The Reds have previously been interested in the Croatian footballer who plays in defence for Lyon and have renewed their interest after Jamie Carragher announced he was retiring at the end of the season.
Chelsea have been eyeing up Lovren as a possible replacement for David Luiz, should the Brazilian leave in June, and he has also been watched by Everton who are also in need of defensive reinforcements.
Elsewhere at Anfield, Fiorentina have targeted unlucky Reds striker Borini as part of their summer transfer plans.
Fabio Borini, 21 was bought in the summer by Rodgers after he worked with him at Chelsea and Swansea. Borini hasn’t had a good start at Liverpool and has suffered injury woe and the latest injury is a dislocated shoulder which will keep him out for the rest of the season.
Danele Prade, Fiorentina’s sporting director said: ‘We like Fabio Borini, but it’s hard to see that Liverpool will let him go.’