The Stadio Olimpico side had to settle for seventh spot in the standings last term under Luis Enrique, but the newly-appointed veteran coach is confident the club will be able to compete for domestic glory this time around.
"Can Roma win the Scudetto? Yes, I think so," Zeman stated to Corriere dello Sport when questioned on the Giallorossi's ambitions for the 2012-13 season.
The 65-year-old then went on to discuss Roma's transfer policy, and added that the players are still getting used to his training methods.
"We have plenty of players in our squad, but it's about quality rather than quantity for me. We can still improve the team.
"We are halfway through pre-season and the lads aren't completely accustomed to my methods yet. They have suffered a bit, but you have to learn to suffer in football. I'm pleased with the progress we've made so far."
Zeman replaced Luis Enrique as Roma coach this summer following the Spaniards decision to leave the club.