Budimir has been linked with Real as they seek a cut-price striker addition this summer.
The Croatia international's contract carries an €8m buyout clause.
He told Sportske Novosti: "It's a special season for me. I'm glad to have achieved a symbiosis between club football and national team football, which in a way are two separate worlds.
“I have the utmost respect for Osasuna. I'm very happy where I am and with who I am. Well, I'm clear that I've had a very good season, that I feel good, and I understand there may be some interest. However, the focus was mainly on the national team, now it's on vacation. I'll leave the transfer issue for another topic.”
Regarding the potential role of Croatia captain Luka Modric, who could act as an advisor to help him adapt to Real Madrid, he concluded: "Yes, yes... But we'll leave that for the future."
Modric will leave Real Madrid after the Club World Cup, with a deal settled with AC Milan.