[4] On 25 April 2001, Liverani became the first black Italian footballer to play internationally with the Italy national team,[5] making his debut with the Azzurri in a friendly match against South Africa in Perugia, under the management of Giovanni Trapattoni; the match ended in a 1–0 victory for the Italians.

[9] In spite of his lack of pace, agility, stamina or defensive skills,[10][11] Liverani was a highly creative, reliable and quick-thinking player, who was known in particular for his technique, vision, range of distribution and precise passing with his left foot, which enabled him to create chances for teammates, and made him an excellent assist provider.

[10][13] Following his retirement, Liverani was offered a position as youth coach at Genoa, in charge of the Allievi Regionali B squad, which he accepted on 15 November 2011.

[16] On 7 June 2013, Genoa president Enrico Preziosi announced the appointment of Liverani as new first team manager in place of Davide Ballardini.

[18] On 8 December 2014, Liverani was appointed as manager of English League One team, Leyton Orient on a 2+1⁄2-year contract replacing Mauro Milanese who returned to his role as Sporting Director after eight matches in charge.

[20] On 6 March 2017, Liverani was appointed as manager of Serie B team, Ternana replacing Carmine Gautieri who was sacked after gaining only three points in seven matches.

[30] On 20 December 2022, Liverani was dismissed from his coaching duties following a 1–2 loss at Palermo and a disappointing first half of the season with Cagliari in fourteenth place in the league table.

[31] On 11 February 2024, Liverani was appointed new head coach of the bottom-placed Serie A club Salernitana until the end of the season.