The Italy international joined BVB last year as a replacement for departed hit-man Robert Lewandowski and was tipped to be a big hit under Jurgen Klopp.
However, the form he showed in 2013/14 as he notched 22 Serie A goals for Torino has not been on show in Germany, where both the 25-year-old and Dortmund have struggled – the club are only just clear of the relegation zone.
Reports suggest that the Westfalenstadion outfit are ready to cut their losses on their man, which has alerted Liverpool.
Immobile is valued at around £15m and could go some way to solving Brendan Rodgers’ striker issues – Mario Balotelli, Fabio Borini and Rickie Lambert have all struggled this season.
The nine-time Italy international represented his nation at the World Cup last year, as they slipped out at the group stage, alongside England.