The three will be playing in their last World Cup with only Sangakkara's teammate Jayasuriya having so far tasted World Cup glory, being part of the Sri Lanka side which sensationally clinched the 1996 title.
"I think people who are coming to the end of their careers are going to be the most dangerous players in this World Cup," said the Sri Lanka vice-captain.
"They will be just that bit hungrier to leave that little legacy, that little mark, that personal touch - like 'that was my World Cup'."
Sangakkara believes Jayasuriya, whose early innings big hitting wowed fans 11 years ago, will have another major role to play in the Caribbean when the 2007 World Cup opens on March 11.
"Sanath doesn't want to be in the shadow of any other batsman in the world," Sangakkara told www.cricinfo.com.
"To do that he has got to come out, improve and do the hard work. He is wiling to do the hard work and at 37 he is one of the fittest in the team, he is bowling, fielding well and he is batting for longer.
"Forty-five runs from Sanath make us win 75 percent of matches and that's why we look forward to him giving us a start. Now we know that if he gets that start he goes on to make that big score."
Indian superstar Tendulkar and West Indies skipper Lara will also make their mark, insists Sangakkara.
"I can see Sachin Tendulkar playing more cricket but I don't know until when," he said.
"It's up to the individual player to decide when you retire. But if you miss that window of opportunity to walk out when you are on top it can be disappointing in the long run.
"Sachin has been a fantastic player over the years, a great batsman and an example to watch. He is going to be that much more focused to leave a mark.
"Lara is another one, at home probably his last World Cup."