Los Blancos are four forwards down on their squad from last season, with Karim Benzema, Marco Asensio, Mariano Diaz and Eden Hazard all leaving the club.
As a result, there will be a lot of movement at Bernabeu this summer in terms of incomings, and there have been suggestions that Chukwueze is a target for Carlo Ancelotti's side.
The Nigeria international made 50 appearances for Villarreal during the 2022-23 campaign, contributing 13 goals and 11 assists in the process.
The 24-year-old only has a year left to run on his contract with the Yellow Submarine, and there have been claims that he could be available for around €40m (£34.3m) this summer.
Chukwueze is ignoring the speculation surrounding his future, though, with the forward only focusing on Villarreal.
"People are always going to talk. I only think about Villarreal. I don't read what they put on social media. That doesn't matter. What matters is the moment," Chukwueze told Panenka.
"What if it's a lie? What if it's not real? I don't know. For now, I don't think it's true. The only thing that is real is Villarreal."
Chukwueze starred against Real Madrid at Bernabeu in April, scoring a brace in a 3-2 Villarreal win, and the forward added that it was "a dream come true" to find the back of the net in the famous stadium.
"It's a dream come true. Who hasn't dreamt of scoring a goal at the Bernabeu? Well, I scored two! It was historic for me and for Villarreal," he said.
Chukwueze made his first-team debut for Villarreal in 2018, and he has now represented the club on 207 occasions, scoring 37 goals and registering 31 assists.
The forward has garnered Champions League experience during his time with the Yellow Submarine, featuring on nine occasions in the competition, scoring twice.
Chukwueze has also played in the Europa League and Europa Conference League for the club, while he has featured on 155 occasions in La Liga, contributing 21 goals and 18 assists in the process.