The youngster has earned comparisons to Andy Robertson and attracted attention from major European clubs.
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Dorgu, 18, broke into the Lecce first team this season and has made eight appearances in Serie A.
And he has already impressed enough for Liverpool to begin monitoring his situation, report Gazzetta dello Sport.
Manchester City are also said to be keen on the left-back, who is under contract until 2027.
City could benefit from strengthening with Sergio Gomez the only recognised left-back in the squad following the departure of Joao Cancelo.
The Portuguese joined Barcelona on loan in the summer but the Spanish giants are also keen on Dorgu.
However all three clubs could miss out on the Dane after he revealed his dream is to play for a different Premier League team.
He said: “Chelsea is my dream to play for. I have been a fan of them for over 10 years, so it would be a huge dream to play for them.”
The Blues could be on the lookout for a left-back following the injury to Ben Chilwell.
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Levi Colwill has deputised in his absence but is more suited to playing in central defence, while boss Mauricio Pochettino has not been keen on using Marc Cucurella.