A 1-0 victory over Bologna on Saturday took Roma, who have lost just one league game this season, to within six points of Juventus ahead of the leaders' match against Torino on Sunday.
Midfielder De Rossi does not know if Juventus will suffer a dip in form, but the Italy international is hoping his side can capitalise should an opportunity arise.
"I don't know if Juventus will start to drop points now or if it'll be a spectacular end to the season, but we just need to win and hope they and (third-placed) Napoli drop points," De Rossi told Rai Sport.
"You can tell it's a good season from lots of little things - in the summer with those who arrived; winning the derby in week four; the fundamental victory in Udinese; the run of results after our defeat (to Juventus) in Turin.
"It is already impressive that we are so close to a team that was constructed to destroy all competition in the league."
Roma's lofty standing represents a far cry from last season when they stumbled their way to sixth position.
On the Bologna win, De Rossi added: "We sent out a message that this is a completely different Roma.
"In the past these games have been turning points and we tended to fall apart, but not this time.
"I saw a team that is focused and very strong. Don't forget Napoli drew here a few weeks ago."
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