Toni Kroos's retirement has led to claims that Los Blancos may bring in a new central midfielder ahead of the 2024-25 campaign, with Veerman thought to be a target.
However, the 25-year-old, who is currently with the Netherlands squad at Euro 2024, has played down the speculation lining him with a switch to the Spanish capital.
Veerman was in impressive form for PSV during the 2023-24 campaign, scoring seven goals and registering 19 assists in 41 appearances in all competitions.
The midfielder managed five goals and 16 assists in 29 Eredivisie outings, while he also featured seven times in the Champions League, with his Dutch club reaching the last-16 stage of the competition.
Veerman plays down Real Madrid speculation
"None of the rumours are true. I could be happy about the fact that they put me in Madrid, but I feel uncomfortable because it is a lie," Veerman told reporters.
"I get tired and uncomfortable in equal measure. Especially, because I have to constantly answer this question when there is absolutely nothing.
"I'm faced with this because someone on TV says I would fit in well there and a Spanish newspaper writes something. Maybe I would fit in there, but hey, it's Real Madrid. When you see the players they have as starters.
"If I leave, it will be to a club that likes to have the ball. I'm not a player who stays back and chases the ball for the whole game."
Veerman, who has a contract with PSV until June 2026, has represented his current side on 115 occasions in all competitions, scoring 22 goals and registering 40 assists in the process.
Will Real Madrid sign a new central midfielder this summer?
Real Madrid will lose Kroos this summer, which is a huge blow, but it would not be a surprise if they did not bring in a replacement for him during the current market.
Indeed, Luka Modric is set to sign a new one-year contract, while there is also set to be a change of position for Jude Bellingham during the 2024-25 campaign.
Kylian Mbappe, who will officially arrive at Bernabeu at the start of July, is expected to play in a front three with Rodrygo and Vinicius Junior next term.
Bellingham, who has operated as a number 10 since his arrival from Borussia Dortmund, is then likely to revert into central midfield alongside Aurelien Tchouameni and Federico Valverde.
Real Madrid are also allegedly pushing ahead with their plans to bring in Alphonso Davies from Bayern Munich, but it remains to be seen whether they can reach an agreement with the Bundesliga giants.