Costa is with Portugal's World Cup squad but has yet to feature in the tournament. He is understood to have only one intention this summer: a move away from Son Moix.
While his preferred destination is a Premier League club, a reunion with Demichelis at RB Leipzig — who will play in the Champions League next season — is also an appealing option, according to those around the player.
Fabrizio Romano confirmed Demichelis has put Costa's name forward, with the defensive midfielder having been a significant presence in the Mallorca side that narrowly survived relegation during the Argentine's final months in charge. Costa finished the season with seven goals in 36 appearances across all competitions — an outstanding return for a player in his position.
Mallorca are asking for a minimum of €20m to open negotiations, a figure that could rise given Costa's strong second half of the season.
He has been at the club since 2023, initially joining from Almería via Braga, with Almería retaining a 20 per cent sell-on clause from that original move.
Costa's contract at Mallorca runs until 2028, giving the club strong leverage. His profile — high-energy, technically composed and capable of arriving late into goal-scoring positions — would suit Leipzig's pressing-based system under Demichelis. The manager's personal advocacy is likely to prove a significant factor in any deal.