Los Blancos are looking to tie veteran stars like Toni Kroos, Luka Modric and Karim Benzema down to new deals beyond the summer while also adding young players to their strong core.
90min reports that while Jude Bellingham is one of Real Madrid’s top targets, they are also looking to recruit Veiga.
The 20-year-old has enjoyed a stellar breakout season at Balaidos, scoring nine goals and laying on four assists in La Liga this term.
Celta Vigo travel to the Santiago Bernabeu to take on Real Madrid on Saturday night, and Ancelotti was asked in a press conference whether he liked the look of Veiga.
“Yes, I like him,” Ancelotti admitted.
“They [Celta] have quality players, like Iago Aspas, who are doing very well.
“We have a lot of respect for Celta, they come with good dynamics. They have organisation and the individualities of Aspas and Veiga.”
Though Real Madrid are firmly in the race to sign Veiga – who has a €40m release clause – there are several other sides fighting for his signature.
90min understands that representatives from Liverpool, Manchester City, Manchester United, Newcastle United and Tottenham Hotspur all watched Veiga during Celta Vigo’s loss to Mallorca on Monday.
Other Premier League teams in Arsenal, Brentford, Brighton and Chelsea have also watched him this season.
