The 23-year-old is on the radar of several top clubs in Europe after finding the back of the net 16 times in 36 Serie A appearances last term - only five players had more in the Italian top flight.
Sassuolo can afford to command a hefty fee for Scamacca's services, though, as the striker signed a new deal with the Neroverdi until 2026 back in April.
Nevertheless, Arsenal are reported to have already lodged a £35m bid for Scamacca, who turned down the chance to move to the Emirates due to his desire to remain in Italy.
The Gunners are not expected to give up their pursuit of the Italy international, but according to Sky Italia - via GFFN - PSG have now entered the race for his signature.
The report claims that the Ligue 1 champions have already held talks over the possibility of bringing Scamacca to the Parc des Princes, but it will take some convincing for the player to leave Serie A.
Furthermore, rumours of a £35m bid from Arsenal have since been rejected by Sassuolo director Giovanni Carnevali, although he has admitted that clubs are beginning to take notice of Scamacca.
"There's nothing concrete yet for Scamacca, just some contacts with some clubs. Of course, after playing with the National team the interest is now growing," Carnevali told Sky Italia.
Scamacca - a former Lazio, Roma and PSV youth prospect - earned his fifth cap for Italy in last week's Nations League draw with Germany but is still waiting for his first goal for the Azzurri.
PSG's need for attacking reinforcements has lessened after Kylian Mbappe signed a new three-year deal at the club, but Mauro Icardi's future has been called into question.
The 29-year-old has two years left to run on his contract and only managed four goals in 24 Ligue 1 appearances last term, but he issued a defiant response amid speculation over his situation in Paris.
"I'm still under contract with PSG for the next two seasons. My career is not in danger, contrary to what you journalists suggest," Icardi wrote on social media.
"It is I who will decide to stay and make myself available to the club... Don't worry, I'm only 29 and people remember very well what I can do after almost 200 goals."
Meanwhile, Arsenal are on the hunt for replacements for Pierre-Emerick Aubameyang and Alexandre Lacazette, the latter of whom will depart after a five-year spell at the end of the month.
Eddie Nketiah is poised to sign a new five-year deal at the club after a strong end to the season, but Mikel Arteta will likely welcome one or two new centre-forwards to North London amid persistent links with Manchester City's Gabriel Jesus.
Arsenal have supposedly already agreed personal terms with the 25-year-old, although Tottenham Hotspur, Atletico Madrid and Real Madrid are also rumoured to be keeping tabs on Jesus's situation.