Talks were held over the weekend, and a loan-to-buy deal is possible in the January transfer window.
A quick, technical right-winger, Laquintana currently plays his football with Brazilian top-flight outfit Red Bull Bragantino, where he is contracted until the end of 2027.
He made 34 appearances for the club in 2025, contributing to nine goals.
Capped twice by Uruguay, Laquintana is eager to secure a berth in their 2026 World Cup squad.
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The 26-year-old is happy to join Celtic and would become the second Uruguayan in their ranks, with Marcelo Saracchi joining on loan from Boca Juniors in the summer.
When fit, the left-back has impressed in green and white, and it is hoped Laquintana could make a similar impact in attack.
Celtic have already signed Mexico defender Julian Araujo on loan this month. He made his debut in Saturday’s 3-1 defeat to Rangers.
Steve Moreira, the 2024 MLS defender of the year who played under Wilfried Nancy at Columbus Crew, was pictured in the Parkhead stands during the match.
Regarding departures, Jahmai Simpson-Pusey is expected to join FC Koln in the German Bundesliga after being recalled by Manchester City, while Hayato Inamura has departed on loan to FC Tokyo, having made just one competitive Celtic appearance.