Though Juve have focused on a number of forwards this summer, sources have told Goal that the Serie A champions now have the Uruguayan at the top of their wish list.
The 33-year-old is heading for the exit at Barcelona, as new head coach Ronald Koeman has informed him that he does not feature in his plans moving forward.
Barca could opt to terminate Suarez's contract at Camp Nou, which would cost the club €14 million (£12m/$17m).
Much like Barcelona, Juventus have a new manager who previously starred for the team and, as Koeman has also done, Andrea Pirlo has recently informed one of his veteran strikers that he is not in his plans.
New Juve boss Pirlo has told forward Gonzalo Higuain that he is free to find another club this summer, along with German midfielder Sami Khedira.
As the Serie A giants search for a replacement for Higuain they have zeroed in on Suarez, who scored 21 goals in 36 appearances for the Blaugrana in 2019-20.
After Barcelona's first trophyless season in 12 years, though, Koeman is determined to make wholesale changes to the squad and jettison some of his team's veterans.
One veteran Koeman does not want to see leave is Lionel Messi, but the Barcelona icon appears set on a departure from a club he has called home for 20 years.
Juventus, meanwhile, are focused on winning the Champions League for the first time since the 1995-96 season after they took home Serie A in 2019-20 for an incredible ninth straight campaign.
Though Pirlo and Co. looked to be eyeing Roma's Edin Dzeko as a replacement for Higuain, they have now fully turned their attention toward Suarez.