On the back of scoring 16 goals in Serie A last season, Scamacca is being heavily linked with a switch to a top European club.
While a transfer to the Premier League now appears increasingly unlikely, PSG seemingly remain in the hunt for the Italy international.
According to Gazzetta dello Sport, PSG have failed with a proposal worth €40m (£33.86m), Sassuolo instead wanting to receive closer to €50m (£42.32m).
However, the report adds that the relevant parties may eventually settle on a fee inbetween those figures, while Scamacca is said to be ready to pen a long-term contract at Parc des Princes.
Alvaro Morata is another forward who has been on the market with Juventus having failed to take up their option to sign the Atletico Madrid forward on a permanent deal.
The 29-year-old has naturally been linked with a wide range of different European clubs, including Arsenal before the Gunners eventually signed Gabriel Jesus.
Nevertheless, the Spain international has now revealed that he intends to spend the 2022-23 campaign at Wanda Metropolitano, effectively acting as a replacement for Luis Suarez.
Speaking to the club's official website, Morata said: "I'm very motivated and I can't wait to start training. I'm sure it's going to be a great year.
"I'm lucky to have already worked with [Diego] Simeone and his team and that will make things easier. I can't wait to start preparing for this season together."
Meanwhile, Norwich City are currently preparing for another year in the Championship after being relegated from the Premier League with a whimper in 2021-22.
Rather than being proactive in the transfer market, Canaries boss Dean Smith has only made one new signing thus far, that player being Newcastle United midfielder Isaac Hayden.
However, according to AS, Norwich are one of three clubs who are interested in securing the signature of Manchester City forward Marlos Moreno.
The 25-year-old has never made an appearance for the Premier League giants, the most recent of seven loan spells being spent in the Belgian top flight with Kortrijk.
With just a year remaining on the Colombian's contract, Man City are happy to part ways with the attacker on a permanent basis over the coming weeks, with Bristol City and Sunderland also monitoring the situation.
Wolverhampton Wanderers supporters are being left frustrated by their club's lack of incomings this summer, but another two fringe players departed Molineux on Saturday.
Meritan Shabani and Renat Dadashov have both been allowed to sign for Grasshopper Zurich on permanent deals after being deemed surplus to requirements.
Shabani's only first-team appearance for Wolves lasted just 10 minutes, the playmaker suffering an ACL injury during an EFL Cup tie with Reading in September 2019.
Meanwhile, Dadashov failed to make a single first-team outing for the West Midlands outfit, the Azerbaijan international spending 2021-22 on loan at Portuguese side Tondela.