Muralitharan has captured 70 of his World record 723 Test wickets against West Indies at 17.34 runs apiece in 10 Tests.
"Murali's record speaks for itself and I'm sure if he bowls well we are going to be right in the game, no doubt about it," Bayliss said.
"We will be hard to beat if he bowls well. Guyana pitches take a bit of turn, but we will take a look at all pitches on the morning of the game and see where we go from there.
"We have two spinners on this tour and if we meet pitches which turn we have options there."
Though Sri Lanka are without fast bowlers Lasith Malinga, Dilhara Fernando, and Farveez Maharoof, Bayliss is satisfied with the composition of his side's bowling attack and believes the key to winning will be the batting.
"Our main concern has been our batting," he said. "We showed in the Test series at home against England recently that we can bat well. If we score enough runs, we will always have the chance to establish winning positions.
"What we want to do is concentrate on what we do best and not worry too much about what the opposition is doing. The guys play to their best when that happens and we have to keep the focus on our game. Of course, we will look at the opponents and their strengths and weaknesses but most of our concentration will be on what we do well."
The first Test takes place at the National Stadium just outside the Guyanacapital from March 22 to 26, and the second Test is set for Queen's Park
Oval in Trinidad from April 3 to 7.
Sri Lanka open their tour on Monday when they face a West Indies Select XI in a three-day match at the Guyana National Stadium.