After working his way through the youth ranks at Sporting, Chermiti broke into the first team during the 2022-23 campaign.
The 19-year-old made his professional debut as a late substitute in January's Lisbon derby against bitter rivals Benfica.
The youngster's first senior goal arrived in a narrow 1-0 win over Rio Ave in February, before going on to find the net in meetings with Porto and Pacos Ferreira.
After gaining valuable first-team experience, Chermiti ended the season with three goals and two assists in 22 competitive appearances.
The teenager's progress has seemingly been tracked by at least two Premier League clubs, with Bournemouth and Wolves believed to be showing an interest.
According to Portuguese outlet Record, via Sports Witness, Bournemouth are leading Wolves in the pursuit of Chermiti's signature.
The South-coast Club are believed to be preparing to formalise their interest by making their first official offer, while Wolves are keeping tabs on the player's situation.
With four years left to run on the player's contract, Sporting are in a strong position when it comes to negotiating a deal.
The report claims that they are prepared to sell their academy product and have now set out their financial demands.
Ruben Amorim's side are looking to receive a €20m (£17.2m) fee and include a 20% sell-on clause in any potential transfer.
Bournemouth have already been busy in the summer transfer window, recruiting Hamed Traore, Milos Kerkez, Justin Kluivert and Andrei Radu.
Chermiti would bolster Andoni Iraola's centre-forward options, with Dominic Solanke, Antoine Semenyo and Kieffer Moore currently available to the Bournemouth boss.