The newly-promoted Ligue 1 side has turned its attention toward luring the Brazil international away from Russia, claims the player's representative.
The 26-year-old has endured a turbulent first spell in Russian football following his move from Porto in September.
And Hulk, who had a transfer request rejected in January because of UEFA regulations forbidding a player appearing for three different clubs in the same season, is said to be attracted to the project currently being developed at the Principality this summer.
According to the player's agent, Teodora Fonseca, the interest is mutual. "I know people at Monaco. They have not contacted me, but there has been speculation and the interest is real," he told Le 10 Sport.
Should a move materialize, Hulk would be reunited with former Porto team-mate Radamel Falcao who is expected to complete his big money move to Claudio Ranieri's men in the coming days.
Earlier in the week, Monaco wrapped up the signings of Porto duo James Rodriguez and Joao Moutinho for a combined fee of 70 million euros.