Sources have told ESPN Argentina's Diego Monroig the Major League Soccer side submitted an offer for the forward over the weekend but Boca believed it to be "insufficient."
MLS sources, however, would not confirm the $16m figure and say it is not accurate.
Pavon, 23, didn't train with the rest of the team on Tuesday and has been left out of the Boca squad to face Athletico Paranaense in the quarterfinals of the Copa Libertadores on Wednesday amid links with a move away.
Boca value the forward at $24m and sources have told ESPN Argentina negotiations between the two clubs have now ended.
"Pavon is a player who has suffered a drop in his form, but nobody forgets how to play football. Because of that, I prefer to loan him to a good European club rather than [agree to] a bad transfer [deal]," Boca president Daniel Angelici told Los Más Grandes on Tuesday.
Sources have said Galaxy have turned their attention to Independiente forward Martin Benitez as an alternative option.
Clarin reported that Benitez's release clause is $20m and that Independiente will only start negotiating at $8m.
Pavon was part of the Argentina squad in the 2018 World Cup in Russia and scored four goals in 19 appearances for Boca last season.