The Reds are currently at the top of the table with a two-point lead over Chelsea.
After Sunday's 4-0 rout over Tottenham Hotspur, Liverpool are in with a strong shot of lifting the coveted trophy.
"It's great oxygen for us, as a team and management," Rodgers told the club's official website. "It's great that the supporters have got that belief - that's so important for them, it's vital that they feel they can dream.
"For us, our focus and composure and mentality is just to work hard, because there's a process to dreaming. You've got to get the work done, or else it doesn't happen."
The Reds will take on West Ham United at Upton Park on Sunday.