Gabriele Sandri, 26, was shot by a policeman at a motorway service station near Arezzo on November 11 last year after a scuffle broke out between rival fans on their way to matches.
The death was one of several violent incidents in Italian football in recent years with decaying stadiums being blamed for fostering an environment of delinquency among 'ultra' fans.
Inter Milan are considering leaving the San Siro while plans are afoot for Rome's top-flight clubs AS Roma and Lazio, who share the imposing Olympic Stadium, to have their own family-friendly grounds.
A fund has been set up to educate supporters on how to behave and Rome mayor Gianni Alemanno wants to go further.
"We hope to contribute by building two stadiums," he told a news conference while on a visit to Poland.
"Being a supporter can turn into something tragic and it's necessary to honour a commitment and do justice to this guy."
Rome's Stadio Olimpico is due to host next year's Champions League final on May 27 but European football's governing body UEFA has said the showpiece could be taken away from the city if serious violence occurs beforehand.
Italy lost out on hosting Euro 2012 partly because of its hooligan problem and non-fatal stabbings by roving gangs armed with flick-knives happen on and off around the Olimpico.
The police officer who shot Sandri, Luigi Spaccarotella, is due to stand trial for murder, with a second preliminary hearing scheduled to take place in January.
He did not attend the first hearing in September because he feared reprisals from hardline Lazio fans.
