Goretzka, 31, will leave Bayern Munich as a free agent when his contract expires in June. Bayern confirmed in January that the deal would not be renewed, and Goretzka himself said he had decided to seek a new challenge.
According to La Gazzetta dello Sport and transfer journalist Gianluca Di Marzio, "positive signs" have emerged from negotiations, with Milan leading the race ahead of Juventus, Napoli, Inter, Arsenal, Fenerbahçe and Atlético Madrid, who had also expressed interest in the winter window but were turned down.
Milan's offer is a three-year deal with an option for a fourth year — longer than competing proposals. Goretzka currently earns significantly more at Bayern and will need to accept a reduction, but the Gazzetta reports the Italian club is making their most compelling possible offer to win the race.
The pursuit of Sørloth tells a different story. The 30-year-old Norway striker has scored 17 goals in 48 appearances for Atlético Madrid this season but has not been a guaranteed starter under Diego Simeone, who is understood to prefer a different physical profile.
According to the Gazzetta, Sørloth wants more regular playing time and would listen to Milan's proposal. Atlético's opening asking price is €40 million including bonuses, but Milan believe that figure will drop to closer to €20-25 million if the Norwegian has a modest end to the season and World Cup.
Head coach Massimiliano Allegri is understood to have specifically requested both signings. Goretzka is seen as a box-to-box addition in the Adrien Rabiot mould, while Sørloth addresses a genuine gap at the top of the attack after Santiago Giménez and Christopher Nkunku failed to convince in their debut seasons.