Costa, 31, had been on loan at Gremio from Italian giants Juventus. But following Gremio's relegation to Serie B last month, the club is facing a significant cut to its finances, and Costa is close to terminating his loan.
One source said that negotiations between Costa and the Galaxy were "moving along" but not done yet. The Galaxy are in need of bolstering their midfield following the offseason departures of Jonathan dos Santos to Club America and Sebastian Lletget via a trade to the New England Revolution, even after they acquired Marky Delgado from Toronto FC earlier on Friday.
Costa has played for some of the world's biggest clubs. In addition to his time at Juve, he had two separate stints with Bayern Munich. He began his pro career with Gremio in 2008 before securing a move to Ukrainian side Shakhtar Donetsk in 2010.
After spending five seasons in Donetsk, during which he won 11 trophies, Costa made the move to Bayern where he spent the next two campaigns. During his time in Munich, Costa won two Bundesliga titles as well as a DFB-Pokal. His stint in Turin was also prolific, winning three Serie A titles. A loan stint at Bayern during the 2020-21 saw him claim another Bundesliga title. He returned to Gremio on loan, but couldn't prevent the club's first relegation since 2004. All told he made 462 league and cup appearances scoring 68 goals.
At international level, Costa has made 31 appearances for Brazil, scoring three goals. He was part of the squad that reached the quarterfinals of the 2018 World Cup in Russia.