General Bantz Craddock, outgoing commander of the US Southern Command, said the 14 were undergoing a 30-day "orientation" at the detention centre but would be available to ICRC representatives when it ends.
"I think it's going to be 30 days from the time we got them, which was around the 1st of September. I guess it'll be the first of October," Craddock said.
A spokeswoman in Geneva said the ICRC was planning a visit to Guantanamo next week.
"They will have the same opportunity as we do pretty much with all the other detainees," General Craddock said. Asked whether that would include private meetings, he said, "I think so".
The 14 include top al-Qaeda leaders captured after the September 11, 2001, attacks on the United States, which killed nearly 3,000 people.
Hicks’ inclusion unclear
President George Bush revealed in a speech earlier this month that they had been turned over to the military at Guantanamo after being subjected to special interrogations at secret CIA prisons.
Asked about their condition, Craddock said they were physically in good shape, but could not say what kind of mental condition they were in.
"We have to get through this orientation, acclimatisation period. We've got to understand their response, because they're in a new environment. We've got to get a feel for how they respond. It's different," he said.
General Craddock said he did not know whether other detainees were aware the new arrivals were there or whether Australian detainee, David Hicks, is among those who Red Cross will be allowed to see.
The ICRC is the only agency allowed by the United States to carry out confidential checks on conditions for detainees held at Guantanamo under its internationally recognised role as the guardian of the Geneva Conventions.
Antonella Notari, a spokeswoman for the Red Cross, said the agency received assurances that it would be able to see the new detainees under its standard conditions, which include access to all areas of the detention centre and private interviews with each detainee.
An ICRC team will arrive at the US military detention facility on Monday to carry out their regular two-week round of visits to detainees.