"What is the BCCI's locus standi? How can we assure the United Cricket Board of South Africa (UCBSA) regarding police matters?," Dalmiya said on Tuesday when told South Africa was worried the two players may be questioned by police during the November tour.
Delhi police had framed match-fixing charges against former South African captain Hansie Cronje, Gibbs and Boje soon after South Africa's last tour of India in 2000.
Cronje, who later admitted to accepting money from bookmakers and was banned from the game for life, died in a plane crash in 2002. Gibbs has already served a six-month ban by South African cricket authorities for the same offence.
Delhi police commissioner K.K. Paul, who investigated the match-fixing scandal, confirmed that the cases against Gibbs and Boje had not been closed.
"The case is obviously open," Paul said. "But it's all too early to give any guarantees that no police action will be taken. Especially because no one has bothered to get in touch with us."
The Pretoria News had reported on Tuesday that UCBSA had written to Indian authorities to "clarify" the matter.
"We wrote to the BCCI in March and asked them to clarify the issue," UCBSA spokesman Gerald de Kock said.
"They replied to us that they did not think there would be a problem," he said. "We wrote them another letter two weeks ago saying we required something more definite and we are waiting to hear from them."
De Kock refused to spell out what the UCBSA's stand would be if the Indian police decided to grill the pair, saying: "We will cross that bridge when it comes."
South Africa are due to tour India in November for an unspecified number of matches. There is speculation that the original plan to have both Tests and One-dayers may be downgraded to seven One-day Internationals due to lack of time.
The BCCI is expected to announce the South African team's itinerary later this month.