Off-spinner Muralitharan needs just nine more wickets in next month's two Tests in Australia to break the retired leg-spinner Shane Warne's world mark of 708 wickets.
"I've spoken to Murali and his sentiments are that he will break the record whether it will be in Australia or elsewhere," Jayawardene told the Colombo-based Nation newspaper on Sunday.
"For him, the Australian tour is about performing well and winning. Down the line, if he can break the record it will be great, but even if he doesn't break it, it is not an issue for us."
Muralitharan will have three more Tests against England at home in December to achieve the feat in 2007 if he fails to set the record in Australia.
Sri Lanka may not have won a Test match in Australia but Jayawardene said his side had the bowlers to end the drought.
"The best chance we have got would be right now because we have a good bowling attack," he said. "We feel that with the attack we've got, we can take 20 wickets. That's the most important thing in winning a Test match.
"The last time (in 2004) we were there, we drew a Test match. I think we are getting closer and closer. Mentally, we are a very strong unit and the guys have developed themselves very well."
Jayawardene said his team was better-prepared to test top-ranked Australia since they had tasted successes in away matches in recent years.
"We've done that in England and New Zealand. Our next goal would be to do that in Australia," he said.
"We have given responsibility to individuals and over a period of time they've realised that they are responsible for their performances.
"It is not just oriented around a few players, everyone has to contribute.
"We've given them that confidence. That's why we've started performing well overseas on a consistent basis. If we can keep that mentality and a strong mind frame, our chances are very good."
The Sri Lankan captain said Australia would still be formidable despite the absence of their match-winning bowling duo of Glenn McGrath and Warne, who quit Test cricket early this year.
"The bowlers they have are a good unit but not as experienced as when they had McGrath and Warne. They are still a very good all-round side. We have to respect that and challenge them in all departments," said Jayawardene.
Sri Lanka leave for Australia on Tuesday with the first Test starting in Brisbane on November 8. The second Test will be played in Hobart from November 16.