The 24-year-old has been in impressive form for his Ligue 1 club during the 2021-22 campaign, providing seven assists in 17 appearances in all competitions.
Henrique still has four years left to run on his current deal, but there was speculation surrounding the Brazilian during the summer transfer window.
According to AS, Barcelona have been interested in the left-back for some time and are now preparing to move for the South American in 2022 despite their financial problems.
The report claims that a bid in the region of €30m (£25.3m) is likely to be enough to convince Monaco to let the defender leave either in January or at the end of the 2021-22 campaign.
Henrique, who previously said that it was "a great pleasure" to be linked with a move to Camp Nou, started his professional career with Atletico Madrid but only made one first-team appearance for the capital outfit before joining Monaco on a permanent deal in 2020. body check tags ::