Georginio Wijnaldum's future took a recent swerve as he signed for Paris Saint-Germain after appearing to have wrapped up a deal to sign for Barcelona after departing Liverpool at the end of last season.
Liverpool are tipped to make more signings this summer after the arrival of Ibrahima Konate, and a replacement for Wijnaldum looks to be on their list.
The 24 year-old has yet to sign a new deal with the Italian side as new manager Jose Mourinho is planning to make new additions to Roma's midfield.
Pellegrini scored 11 goals and made nine assists in all competitions last season and could add a more creative outlet in midfield for Liverpool next season.
David Maddock of the Daily Mirror recently reported the Italy international is primed for a move to Liverpool.
The speculation surrounding a deal for Pellegrini will be met with some caution from fans as recent reports suggest the midfielder wants to remain in Rome as Jose Mourinho will undoubtedly want to make a title charge to challenge Inter Milan next season.
Lorenzo Pellegrini is not the only midfielder to be linked with Liverpool in recent weeks. The Reds also have apparent interest in Raphinia, Yves Bissouma and Youri Tielemans.
These links could well be pure speculation due to the departure of Gini Wijnaldum, but it will give fans cause to be optimistic that Liverpool will add to the middle of the park this summer.