Spinner Vettori and fast bowler Southee along with all-rounder Rob Nicol have been suffering from sickness and New Zealand captain Ross Taylor earlier said that the team were unsure about their availability for the match at Pallekele.
"They took part in training today," New Zealand media manager Ellery Tappin told Reuters.
"They obviously have low immunity, but they went through the training well. Highly likely they will be available for the match tomorrow (Friday)."
New Zealand face Pakistan on Sunday at the same venue. The two top teams will advance to the super eight stage.