The 20-year-old began his career with Progreso where he made his professional debut as a 17-year-old before moving across Montevideo to join city rivals Liverpool at the beginning of 2023.
Rodriguez has since developed into a first-team regular for Liverpool, scoring 14 goals and registering six assists in 44 appearances across all competitions.
The winger contributed with nine goals and six assists in his debut campaign with Liverpool to help the Uruguayan outfit win their first-ever top-flight title last year.
Rodriguez has since made a bright start to 2024, scoring four times in eight games including his first goal in the Copa Libertadores last week, while he was handed his senior international debut by Uruguay boss Marcelo Bielsa in March.
Luciano Rodriguez emerges as transfer target for Man City
According to Fichajes, Guardiola has asked Man City to step up their pursuit of Rodriguez ahead of the summer transfer window.
The report claims that Rodriguez has emerged as one of the Citizens' main transfer targets, although they face competition from Eredivisie giants Feyenoord.
It is understood that the rapid rise of the highly-rated winger both at club and international level has caught the eye of a number of top clubs including Man City and Feyenoord.
Earlier this year, Chelsea were credited with an interest in Rodriguez, who is under contract at Liverpool until December 2027.
Man City familiar with South American market
A plethora of South American stars have represented Man City over the years, with the likes of Sergio Aguero, Pablo Zabaleta, Carlos Tevez, Fernandinho and Ederson among those to have etched their names into the club's history.
In recent times, the Citizens have delved into the Argentine market and most notably lured Julian Alvarez away from River Plate in 2022, with the forward having since gone on to establish himself as a first-team regular under Guardiola as well as win the World Cup with Argentina.
Man City have already reached an agreement to sign another highly-rated youngster from River Plate in the form of 18-year-old Claudio Echeverri, who will make the move to the Etihad Stadium this summer.
The Citizens are also said to among a number of top European teams battling for the signature of River Plate's 16-year-old midfielder Franco Mastantuono.