Alisson became the second Roma player to make the switch to Liverpool in the last two summers, following in the footsteps of Mo Salah.
Roma regretted the sale of Salah last season, and not just because his price tag of €42m was criminally low. He returned to haunt them in the Champions League, scoring twice when Liverpool beat I Giallorossi in the semi finals.
Di Francesco hopes for a reunion in 2018/19, this time with Alisson on the other side.
"We hope to meet him in the Champions League and beat him, like I told him today when he came to say goodbye," Di Francesco said, quoted by the Metro.
Roma and Liverpool are ranked very close together in the UEFA coefficients, so it's possible that they might be in the same pot when the draw is made for the group stages, which would keep them apart until the last 16 at the earliest.
Liverpool won 5-2 at Anfield in last year's competition, a deficit which Roma were unable to overturn at the Stadio Olimpico despite winning 4-2.
The Reds went on to lose the final to Real Madrid but an impressive summer in the transfer window means that they will fancy their chances of going one step better this coming season.
Alisson is Liverpool's fourth signing of the summer, joining Naby Keita, Fabinho and Xherdan Shaqiri in making the move to Anfield.