Last season's runners-up are full of confidence after they snapped Juventus' 22-match unbeaten run with a 2-0 win at the Stadio San Paolo on Sunday.
Although Juventus are 11 points clear at the summit and on course to retain the Scudetto, the race for second spot is still alive, with six points separating Roma and Napoli.
Roma, one of this season's surprise packets under the guidance of Rudi Garcia, are due to host out-of-form Parma on Wednesday, and defeat could open the door for the dual Serie A champions from Naples with seven matches left to play.
"Everything is possible," Hamsik told his official website. "We will do everything that is in our power.
"There are still seven games to go and we'll see what happens between Roma and Parma.
"It's just a shame we dropped so many points against teams in the lower half of the table."
Incidentally, Napoli are also in action against Roberto Donadoni's Parma this week, making the trip to the Stadio Ennio Tardini on Sunday.
Parma have not beaten Napoli on home soil in Serie A since their crushing 4-0 win in 2001.
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