"We have not been offered it yet, but if we are, we will be more than happy to host it," Dalmiya said on Saturday on the sidelines of the One-day International against Pakistan at the National stadium in Karachi.
"It will be an honour to host the tournament in September this year at a time when we are celebrating 75 years of Indian cricket."
The 12-nation tournament, regarded as a mini World Cup, is due to be held in England from September 10-25, but speculation is rife the ICC may shift the event elsewhere if England decline to tour Zimbabwe in October.
England have delayed confirming the tour, facing strong British Government pressure to scrap the tour in protest at the policies of Zimbabwe President Robert Mugabe.
Under new sanctions agreed at a board meeting of the International Cricket Council (ICC) in Auckland earlier this week, England risk a two million dollar fine if they fail to tour Zimbabwe.
Dalmiya slammed the England Cricket Board (ECB) for showing double standards when it came to imposing penalties on teams refusing to tour other countries.
"When India declined to play against Pakistan in the last three years, England wanted fines to be imposed on us," Dalmiya said.
"Now England do not want to tour, but they do not want to be penalised. I think the ECB has a lot of explaining to do. If England do not go to Zimbabwe, there is a possibility that Zimbabwe could pull out of the Champions Trophy. I don't think a truncated draw is the way to go."
ICC president Ehsan Mani, who flew in with Dalmiya from Auckland to witness the Karachi match, rubbished reports emanating from England that a decision to tour Zimbabwe will only be taken only after the ICC counter-signed the host agreement of the Champions Trophy.
Mani also did not rule out shifting the Champions Trophy out of England in case it did not agree to tour Zimbabwe.
"Shifting is possible," Mani said, but added no decision had been taken to move the tournament out of England.
"England can't delay the Zimbabwe tour decision for long," Mani said. "But in a perfect world, the Champions Trophy should be held in England as scheduled and England should tour Zimbabwe."
The tournament will be contested by the 10 Test-playing nations -- Australia, England, India, Pakistan, Sri Lanka, Bangladesh, New Zealand, South Africa, Zimbabwe and the West Indies -- and Kenya and the United States of America.
Zim Tour: ICC to act tough against Eng