Moody, 41, has revived Sri Lanka since he was appointed in May 2005 and the 1996 champions are among the leading title contenders in the Caribbean.
However, the former Australian all-rounder is seen as a possible successor to England coach Duncan Fletcher, who has been heavily criticised after last year's 5-0 Ashes series rout in Australia.
Fletcher has a rolling contract with the England Cricket Board (ECB).
Jayawardene said Moody had brought a freshness to the team and pushed seniors such as himself, Sanath Jayasuriya and Muttiah Muralitharan.
"That is the decision he has to make," he told reporters when asked about Moody's possible exit.
"We've enjoyed playing under him. The things that he has done is push everyone in the team, from Murali to Sanath to myself to the youngest player in the camp.
"Everyday you try and learn something," he said. "That is something special Tom has brought to this team. Obviously a lot of the guys like the way he handles players as well.
"He wanted to take us to the World Cup and then see where he wants to be," he said. "But it is his decision and we will have to acknowledge that.
"Sri Lanka cricket, whether he stays or not, will not divert from where we are going. If Tom stays back it will be brilliant."
The seven-week World Cup culminates in the Bridgetown, Barbados final on April 28. It is the first to be held in the Caribbean.
