Sri Lanka won the 1996 ICC Cricket World Cup under the leadership of Arjuna Ranatunga and ended-runners up in the last edition in the West Indies.
Muralitharan is confident that what the team could not do in 1999, 2003 and 2007 can be done this time around.
"The day we won the cup in 1996 was the happiest day. It is because of that our cricket has come this far. It's been 15 years since 1996 and we can't dwell in the past. The teams are different. You can never compare generations.
"In 2003 we entered semis and in 2007 we entered finals. We had good teams but we could not win the cup. But this team I think we have a chance," Muralitharan said.
Sri Lanka's first and only title triumph came when it co-hosted the mega event and since this time around also they are playing hosts, captain Kumar Sangakkara says it will work to their advantage.
"I think every Cricket World Cup is a great opportunity to win it no matter where you play. This one playing in our neck of the woods probably gives us a slighter edge than the other teams," the left-handed batsman said.
However, Sri Lanka has two new venues for the World Cup and changes have also been made to the pitch at Premadasa stadium.
The Lankans have not had access to the stadiums because the construction work is still not complete and they would not have much of an idea about the nature of strips.
However, Sangakkara was not worried on that front. "There is no point in us being concerned about that because our mental approach has to be, regardless of getting an experience on the wickets, there is a World Cup to be played and played well," Sangakkara said.