Grant Wahl was the first to report the current state of the talks.
A source added that former San Jose Earthquakes head coach and current Galaxy interim manager Dominic Kinnear is also one of the finalists.
"[There are] still some final details and steps to be taken," the source said, adding that the Galaxy is hoping "all will fall into place."
The position has been vacant ever since Guillermo Barros Schelotto was fired with three games remaining in the 2020 regular season, a campaign that saw the Galaxy fail to make the postseason for the third time in four years. Kinnear, a Galaxy assistant for parts of the last four seasons, took over on an interim basis for the second time in his tenure with the club.
Vanney just recently became available, resigning his position with Toronto on Dec. 1 following a stellar spell with the Reds that lasted parts of seven seasons. Prior to his arrival, Toronto had never qualified for the MLS Cup playoffs, but under Vanney the team became one of the elite sides in MLS.
In 2017, the Reds won a domestic treble of MLS Cup, Supporters Shield and Canadian Championship. Toronto reached the MLS Cup final on two other occasions and also won the Canadian Championship in 2016 and 2018. His overall record with the Reds was 112-82-56.
In announcing his departure from Toronto following a season in which the team had to relocate to Hartford, Connecticut for part of the campaign due to COVID-19-induced travel restrictions, Vanney gave conflicting signals as to how quickly he would return to managing.
On the one hand, he said he wasn't the kind of person to "sit still for very long" but also said he needed a "mental health break." Now it appears that his stint out of management will be very brief.
In L.A., Vanney will attempt to bring the Galaxy back to its former glory, a history that includes five MLS Cups. Vanney spent seven seasons with the Galaxy during his playing career, one that saw him part of sides that won the 1998 Supporters Shield, the 2000 CONCACAF Champions Cup and the 2001 U.S. Open Cup. He also was part of the D.C. United side that won the 2007 Supporters Shield.
At international level, Vanney made 37 appearances for the USMNT, scoring one goal. He was part of the side that claimed the 2005 CONCACAF Gold Cup.