Neil Fissler of the Sunday Express reported Reds manager Jurgen Klopp has been monitoring the prodigious talent and is ready to capture the £35 million-rated Italian ahead of Spurs coach Mauricio Pochettino.
Barella has featured prominently for his country at youth level and appears destined for full international honours after a call-up to the senior squad.
The 21-year-old has previously spent time on loan at Como, but he has established himself for the Sardinians in Serie A.
Per RMC Sport (h/t James Benson of the Daily Express), Liverpool's interest reportedly dates back to the summer, as Klopp splashed the cash after falling short in the UEFA Champions League final.
According to Fissler, AC Milan and Inter Milan hold an interest in the player, but Barella is said to be keen to find his way to the Premier League, opening the door for Liverpool.
The starlet made 34 appearances for his club in Serie A last season, scoring six goals as scouts and pundits took note of the player's talent.
Alex Oxlade-Chamberlain's injury at Liverpool has left Klopp additional space in his squad this season, and Barella has the technique to complement the Reds' current playing staff.
Eurosport journalist Siavoush Fallahi was impressed with the midfielder after Cagliari held Milan to a 1-1 draw in Serie A on Sunday:
Klopp's purchasing has progressively improved since his first year in charge at Anfield, and the recent additions have made his selection robust and healthy.
The young Italian has great ability with free-kicks, and he displays incredible maturity in his defensive duties as a central midfielder.
Barella will quickly outgrow his surroundings at Cagliari, and a transfer to England would suit an ambitious footballer potentially on the cusp of a strong career.