According to Nicola Balice at Calciomercato.com, Juve have "resumed talks" with the Brazilian's representatives, although they are aware Monaco will refuse to sell for less than €50 million.
The club plan to scout Fabinho and full-back Djibril Sidibe and are willing to spend big this summer to strengthen the squad.
Fabinho is a versatile player, able to feature in central midfield or at full-back, and he excelled last season as a key part of Monaco's title-winning side.
WhoScored.com highlight what he brings to the Monaco team:
Per the report, Atletico Madrid, Paris Saint-Germain and both Manchester United and Manchester City all attempted to land Fabinho last summer, only for the 23-year-old to opt to stay at Monaco.
Leonardo Jardim's side have struggled to replicate last season's form; they have managed just one point in three UEFA Champions League games and have already been beaten twice in Ligue 1.
Monaco saw Kylian Mbappe, Tiemoue Bakayoko, Bernardo Silva and Benjamin Mendy all leave in the summer and may be vulnerable to losing more stars if they fail to challenge for honours this season.
Meanwhile, Gimenez has "caught the eye of Bianconeri scouts," according to Tuttosport (h/t Football Italia).
Gimenez is not a regular at Atleti, starting just four La Liga games and only once in the Champions League, per WhoScored.com.
However, like Fabinho, he also has a large release clause in his contract, which runs until 2021, and Juve would need to pay €65 million for his services, per the report.
Gimenez is just 22 but already an experienced defender and could possibly be tempted by the offer of regular football from a top club.
Juventus, meanwhile, have looked uncharacteristically vulnerable in defence this season.
Juventus have had to cope with the departure of Leonardo Bonucci in the summer, and coach Massimiliano Allegri appears to be still searching for the right balance.