Ntini has not fully recovered from a hamstring strain and Pollock has a sore lower back, adding to the Proteas' misery over the absence of regular skipper Graeme Smith, star all-rounder Jacques Kallis and hard-hitting batsman Justin Kemp.
"We will take a decision on Makhaya before the game, but Polly looks doubtful," Boucher said ahead of the day-night game at Premadasa stadium on Monday.
"We won't finalise our team till tomorrow afternoon to give ourselves more time to assess the injury situation."
Boucher took over the one-day captaincy from Ashwell Prince who led the two Test matches on the tour, both of which Sri Lanka won to continue their domination of South Africa at home.
The last time South Africa toured Sri Lanka in 2004, the hosts won the Test series 1-0 and blanked the tourists 5-0 in the one-dayers.
South Africa have won just one of the 11 limited-overs internationals they have played in Sri Lanka against the home team.
Asked if South Africa had finally found the key to defeating Sri Lanka in their own backyard, Boucher quipped: "Let me know if you have any suggestions."
However the gutsy wicket-keeper was confident that his depleted team will put up a good fight in the series that also features India.
"We want to forget that 5-0 defeat two years ago and start a new chapter," said Boucher.
"We are very proud of the fact that we are the number two team in the world rankings (behind Australia) and are keen to build on that.
"We are missing key players but their absence gives the younger players a chance to put their hands up and be counted.
"We have the players to change the game over 50 overs, so it will all depend on how we play on a particular day.
"You can be sure there won't be too many boring games in this series and that should please the fans."
South Africa can take heart from their last one-dayer in April that saw them surpass world champions Australia's 434-4 off the penultimate ball in a sensational one-wicket win at the Wanderers in Johannesburg.
Herschelle Gibbs, who smashed 175 off 111 balls in that match, will spearhead the South African batting in the absence of Smith and Kallis.
Bad weather over the Sri Lankan capital, however, threatens to disrupt the series in which each team plays the other twice in the league before the final on August 29.
The wicket at the Premadasa stadium has been covered for the last three days because of incessant rain, but the ground staff predict a prompt afternoon start if the rain keeps away.
Sri Lanka have also delayed naming their playing 11 due to the uncertain weather.