The Norway international was in excellent form for the Yellow Submarine during the 2023-24 campaign, scoring 26 goals and registering six assists in 41 appearances in all competitions.
Sorloth has a contract with Villarreal until the summer of 2028, but there is currently speculation surrounding his future.
According to AS, West Ham have expressed an interest in signing the 28-year-old during this summer's transfer window, with Roma also allegedly keen.
However, it is alleged that Villarreal are not prepared to let Sorloth leave unless his release clause, thought to be €38m (£32m), is met.
Sorloth turned out for Crystal Palace in the Premier League earlier in this career, but he only managed one goal in 20 appearances during a disappointing spell.
Forest 'looking to sign Adams'
Meanwhile, according to Football Insider, Nottingham Forest are keen to sign Che Adams on a free transfer.
The 27-year-old's contract with Southampton expired at the end of June, so he is currently available on a free, with a number of clubs said to be interested in his signature.
Forest allegedly view Adams as a priority target this summer, but the Reds may have to move quickly if they are to secure his signature ahead of the 2024-25 campaign.
The Scotland international scored 18 times in 46 appearances for the Saints during the 2023-24 campaign.
Meanwhile, the forward has managed 25 goals in 124 Premier League appearances, in addition to registering 13 assists in England's top flight.
Brentford 'open talks over Pavlovic deal'
Elsewhere, Brentford have allegedly opened discussions with Strahinja Pavlovic over a deal for the Red Bull Salzburg defender during this summer's transfer window.
The 23-year-old was a vital player for his Austrian club during the 2023-24 campaign, making 36 appearances in all competitions, including 25 league appearances.
Pavlovic has a contract with Salzburg until June 2027, but he is being strongly linked with a transfer during the current market.
According to transfer expert Fabrizio Romano, Brentford have opened talks with Pavlovic over a switch to the Premier League club this summer.
Romano claims that "many clubs" are interested in Pavlovic, who represented Serbia in the group stage of Euro 2024, including an appearance against England on June 16.