According to MLB.com's Jon Paul Morosi, the Dodgers are "well-situated" to land Vazquez because of their deep minor league system and desire to pair a quality lefty with closer Kenley Jansen in late-game situations.
The Dodgers, who have reached the World Series in each of the past two seasons, own the best record in the majors at 55-26.
Vazquez, 27, has been Pittsburgh's closer for most of the past three seasons. In 31 appearances this season, he is 1-0 with a 1.91 ERA, 1.09 WHIP and 51 strikeouts over 33 innings. He has also converted 19 of his 20 save chances.
The Venezuela native has improved on a 2018 campaign in which he went 4-2 with a 2.70 ERA, 1.24 WHIP, 37 saves and 89 strikeouts in 70 innings en route to his first career All-Star nod.
Vazquez is under contract for two more seasons beyond 2019 with club options in 2022 and 2023 as well. Because of that, the Pirates may not be in any hurry to move on from their star closer.
Pittsburgh is tied for last in the National League Central at 36-41, however, and moving Vazquez would likely yield a strong package of prospects.
The Dodgers are strong offensively and have the best team ERA in the majors at 3.19, but their bullpen ERA only ranks 11th at 4.12. Los Angles also has the ninth-most blown saves this season with 13.
Jansen has not been his usual dominant self with a 3.21 ERA and three blown saves in 26 chances. Among L.A.'s other full-time, regular relievers, Pedro Baez is the only one with a sub-3.00 ERA at 2.80.
The Dodgers don't have many weaknesses, but their bullpen is perhaps their biggest, and it may be the only thing standing in between them and a third straight World Series appearance.