The Danish international is reportedly a key target for the Spanish giants as they plan a summer midfield rebuild.
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In strong form for the Portuguese side, Hjulmand acknowledged the rumours and expressed pride at interest from the 15-time European champions.
"It's a great honour for me to see my name associated with a club like Real Madrid, but I'm at Sporting and I have a lot of love for this club," he said.
"Therefore, my focus is on being here and tomorrow's game. I will talk about my future after tomorrow's game, that's for sure. As for being a starter, I've trained well, but that depends on the manager."