Mourinho wants strong squad rotation as Real Madrid look to compete on all fronts next season, and Veiga, 22, fits the profile the club's sporting department is assessing as a possible reinforcement at the back. The Portugal international is valued at €30 million and signed a long-term contract with Villarreal, running until 2032, when he joined from Chelsea last summer.
Villarreal will look to resist any approach, but are aware of the pull a move to Real Madrid could exert on the player.
Any formal offer remains on hold while Real Madrid work through the exit of Asencio, who has been told by Mourinho that he does not feature in his plans and is among the defenders the club expects to leave this summer. Real Madrid's hierarchy is understood to be waiting for Asencio's situation to resolve, expected in the first days of August, before opening talks with Villarreal over Veiga.
The interest comes as Real Madrid continue to work on multiple fronts. The club has already welcomed Bernardo Silva, Marc Cucurella, Denzel Dumfries and Ibrahima Konaté this summer and has all but completed the signing of Yan Diomandé from RB Leipzig, while separate negotiations with Manchester City over a move for Rodri continue in parallel.
Veiga, who came through Sporting CP's academy before spells at Augsburg, Basel, Chelsea and a loan at Juventus, has made 18 appearances for Portugal and would offer left-footed cover across multiple defensive positions if a deal for him were to progress.
Veiga's versatility — comfortable at centre-back, left-back or in a deeper midfield role — is precisely the kind of profile Mourinho has favoured throughout his career, valuing players who can cover several positions within a smaller matchday squad.
His arrival at Villarreal last summer was itself a significant deal for the Yellow Submarine, and former manager Marcelino has come to rely on him as a regular starter, meaning any departure would be keenly felt in Castellón. For now, though, the move remains firmly tied to developments elsewhere in Real Madrid's squad rather than an active negotiation between the two clubs.