Milan have already signed seven players this summer, including Ruben Loftus-Cheek, Christian Pulisic, Tijjani Reijnders and Noah Okafor.
According to AS, Milan are on the verge of signing the Nigeria international for a fixed €20m (£17.3m) fee plus add-ons.
With 12 months remaining on his current deal, Villarreal have taken the decision to cash in rather than let him leave for nothing next summer.
Should everything go according to plan, Chukwueze will sign a five-year deal with the Rossoneri until the summer of 2028.
The winger will leave the Yellow Submarine after scoring 37 goals and contributing 31 assists in 207 appearances across all competitions.
As for Lazio, they have reportedly joined the race to sign Chelsea winger Callum Hudson-Odoi, who has returned from a disappointing loan spell with Bayer Leverkusen.
Hudson-Odoi is hoping to experience regular playing time next season after being restricted to just seven Bundesliga starts last term.
Chelsea have already rejected a bid from their West London neighbours Fulham, while there has also been interest from the likes of Brentford, Crystal Palace, Nottingham Forest and West Ham United.
However, those Premier League clubs could face further competition, with Alfredo Pedulla reporting that Lazio are considering a move.
Hudson-Odoi is well known to Lazio boss Maurizio Sarri following the Italian's stint as Chelsea boss during the 2018-19 season.
There is a belief that the Serie A side would be looking to sign the 22-year-old on an initial loan deal with an option to buy.
Staying in Italy, Champions League finalists Inter Milan are reportedly keen to secure the services of West Ham striker Gianluca Scamacca.
After pulling out of the race to sign Romelu Lukaku, Inter have made Arsenal's Folarin Balogun their first-choice target.
The Nerazzurri are also considering alternatives in case they fail to land Balogun, and according to The Standard they have identified Scamacca as a potential option.
Despite arriving from Sassuolo in a £35.5m deal last summer, Scamacca is already being linked with a move away after enduring a difficult first season in East London.
Scamacca, who has four years left to run on his contract, recently indicated that he would be open to a move to Roma.
Jose Mourinho's side would prefer to sign the Italy international on a loan deal, which is something West Ham are reluctant to agree to.
Nottingham Forest, meanwhile, are reportedly interested in signing experienced goalkeeper David Soria from Spanish side Getafe.
The Tricky Trees are in the market for a new shot-stopper after Dean Henderson and Keylor Navas returned to their parent clubs at the end of last season.
While discussions are believed to be ongoing over a permanent deal for Henderson, Forest boss Steve Cooper is keen to recruit two goalkeepers this summer.
According to Marca, the Premier League club are targeting Soria, and they are willing to offer between €5 (£4.3m) and €6m (£5.2m) to prise him away from Getafe.
However, Getafe are hoping to receive €10m (£8.7m) for the Spaniard, who was linked with Real Madrid earlier this summer, but a move never materialised.
The 30-year-old, who joined Getafe from Sevilla in 2018, has featured in 185 competitive games during his time with the Azulones.