Italian outlet Calciomercato, as quoted by the Daily Mirror, is reporting that the Reds are pondering a move to sign the Spaniard, who they sold to AC Milan back in January 2015.
The same report even claims that Liverpool FC made a move to try and sign Suso in the January transfer window but failed.
Now, the Reds are said to be lining up a fresh move to sign Suso this summer as Jurgen Klopp looks to strengthen his squad ahead of next season.
Suso only managed to make 15 appearances during his spell at the Merseyside club between 2012 and 2015.
The 24-year-old has been in solid form for AC Milan so far this season, scoring six goals and making five assists in 29 Serie A appearances for the Italian side.
Meanwhile, Liverpool FC are set to take on AS Roma in the Champions League semi-finals as they look to secure a place in the final against either Bayern Munich or Real Madrid.
Liverpool FC are currently in third place in the Premier League table as they seek Champions League qualification for next season.
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