National Aids Trust's chief executive Derek Bodell asked for the meeting with commission chair Trevor Philips following articles published in the Daily Telegraph and other newspapers.
"We are aware there has been an increase in the number of people with HIV over the past four years and a basis for the increase is people who've been infected abroad," Bodell told Third Sector. "But the vast majority of these people are here legally as students or visitors, and only a few of them are refugees or here illegally."
Bodell wants to work with the CRE to launch a low-level strategy to challenge mistaken assumptions that it is refugees and asylum seekers who are behind rising cases of the disease.
"Hopefully we won't need to get into having a joint campaign," he said.
"The fact that two respected organisations have come together and are able to articulate our concerns should be enough to make the Government act, and make the press think about how they are portraying these issues."
He said the trust was increasingly concerned that Aids organisations did not have a strong enough voice to tackle this issue by themselves.
"We need to be part of a broader church," he said.
The commission refused to speculate on what might emerge from the meeting on 7 July, but chair Trevor Philips spoke out against recent newspaper stories which claimed HIV-infected asylum seekers were bringing the health service to breaking point.
"I can't imagine that any British doctor would ever suggest that patients should be treated differently on the basis of their origins," he said.