Sporting president Frederico Varandas has confirmed negotiations are underway, though he stressed a deal is not yet close.
At the Metropolitano, Atletico Madrid have decided the Danish international should be their defensive midfielder. After a summer in which many names have been mentioned, Hjulmand appears to be the club's chosen man.
But as is always the case with Sporting, negotiations will not be straightforward, even though they have now begun, as the Lisbon club's president confirmed.
It is a start. The player's wish remains to wear Atlético's red and white. The exact size of the offer is unclear, though reports from Portugal suggest it could be worth around €40 million. The Portuguese club say they have already rejected an opening offer from Atlético Madrid.
"We received a proposal and we rejected it. It's far from the value we want," Varandas said.
Varandas also stressed that if the player wants to leave, he already knows what offer would need to arrive.
Hjulmand, 27, is Sporting's captain and joined the club from Italian side Lecce in 2023. He has made 141 official appearances for Sporting, scoring 10 goals and providing 12 assists, and has a contract at the club until June 2028. Sporting are believed to value him at between €40 million and €50 million, while reports in Portugal suggest Atlético have already reached an agreement in principle with the midfielder over personal terms on a contract until 2031.
Sporting have already lined up his replacement, with midfielder Sergi Altimira leaving Real Betis for Lisbon, a deal worth more than €20 million for the Andalusian club.
Diego Simeone is understood to see Hjulmand as a player capable of protecting Atlético's defence and adding stability in midfield, an area that has occasionally lacked physical presence over the course of the season.
Everything forms part of the negotiation. One that has only just begun and could be resolved sooner than it appears from the president's comments. These are key weeks for Atlético Madrid as they search for the man to solve their midfield puzzle.