Barca's World Player of the Year Messi passed Germany striker Muller's tally and set a calendar-year scoring record of 86 goals for club and country in 2012 with a double in a 2-1 win at Real Betis in La Liga on Sunday.
It is also 40 years since the Catalans last visited Cordoba.
"In sport anything is possible," said Carlos Gonzalez, president of second tier Cordoba. "But it will be very tough.
"Barca's second team could be runners-up in the league although we would have a better chance with them," he told reporters.
The Andalusian club, who host the last-16 first leg tie, played their penultimate top-flight match against title-chasing Barca before being relegated at the end of the 1971/72 season.
The game at the Arcangel stadium was a pivotal moment in the championship race that year.
Barca headed south, two points behind leaders Real Madrid who had a city derby at Atletico Madrid to contend with.
Atletico trounced Real 4-1 but an already-relegated Cordoba side that included current Spain coach Vicente del Bosque (pictured) in their ranks, on loan from Real, stunned Barca 1-0.
The winning goal was a disputed 54th-minute penalty struck by another Real loan player Fermin who beat Barca's Miguel Reina, a Cordoba local and father of current Liverpool goalkeeper Pepe.
Real Madrid went on to win their final game against Sevilla to secure the championship while Barca slumped to a home defeat by Malaga.
Cordoba have not returned to the top flight since although they made the play-offs last season and are now mid-table in the second tier.
Although they surprised La Liga side Real Sociedad 4-2 on aggregate in the last round, they have suffered two defeats and three draws in their last five outings.
Asked about Barca forward Messi's goal-scoring run, Gonzalez joked: "We have tried to speak to the police to see if they could detain him".
Another second division side, Las Palmas, host Real Betis on Thursday when Levante also entertain Real Zaragoza.
New Valencia coach Ernesto Valverde celebrated his debut at the helm with a 1-0 win at struggling Osasuna in La Liga on Saturday and he returns to Pamplona looking for a repeat in Tuesday's first leg.
Under-pressure Real Mallorca coach Joaquin Caparros is seeking his first win in 13 outings when Sevilla visit on Wednesday, Atletico Madrid host near-neighbours Getafe and league champions Real travel to promoted Celta Vigo.
Third tier Eibar head off to San Mames to play last year's runners-up Athletic Bilbao for a delayed last-32 return match where they defend a 0-0 first-leg result.
The winners meet Malaga in the next round.
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