The plan is the latest in a long list of changes made by the city's new mayor - a former communist judge who ran with left-wing coalition Ahora Madrid - during her first few weeks in the position.
Madrid City Hall announced a "participatory" plan in which neighbourhoods will vote for who they want their streets named after.
According to Spanish daily 20 minutos, Carmena is keen to exchange Francoist street names for those of illustrious women, such as novelist Emilia Pardo Bazán and iconic Republican leader Dolores Ibárruri, known as La Pasionaria.
Another idea is to allow residents of each neighbourhood to vote for which of the area's illustrious residents they would like to see immortalized on street signs.
Over 150 streets, squares and public spaces in Madrid still bear names that commemorate or celebrate the 1936 military coup, the Spanish Civil War and its protagonists, according to a City Hall spokesman.
The City Hall has said their aim is to comply completely with Spain's Historical Memory Law, which was passed in 2007 and included an official condemnation of the Franco regime as well as the removal of Francoist symbols from public buildings and spaces.
Despite the law being passed eight years ago, Madrid's conservative city council had still not removed all the Francoist symbols from the city before May's local elections, which saw the Popular Party lose their 24-year rule of the city in favour of left-wing Carmena.
"The guidelines are to comply with the law, respect the surroundings and that residents participate and give their approval," a source from Madrid's City Hall told 20 minutos.
Madrid still counts several streets named after Francoist soldiers, including General Varela, General Yagüe and General Fanjul as well as two streets that still bear the name of Franco himself: Avenida Comandante Franco in Chamartín (see map, above) and Travesía General Franco in the Carabanchel neighbourhood.
The capital city is not the only place in Spain still maintaining relics of the Francoist past. Dozens of monuments honouring his regime are still scattered across the country 40 years after his death.
Carmena has already foregone several of the privileges normally associated with the position of mayor, choosing to give up her chauffeur-driven car in favour of taking the metro and giving up City Hall's VIP box at Madrid's Las Ventas bullring.
And Franco is not the only name she wants banned from the city; she is currently contemplating renaming Margaret Thatcher square less than a year after it was inaugurated by the previous conservative mayor of the city, Ana Botella.