The JCR, announced last month, is expected to be made up of computer experts who will work alongside regular forces to protect the nation's cyber defences.
JCR head Lt Col Michael White told BBC Newsnight that recruitment of cyber-trained reservists would focus their skills rather than "personality traits".
He said: "I think if they [someone with a criminal record for hacking] could get through the security process, then if they had that capability that we would like, then if the vetting authority was happy with that, why not?
"We're looking at capability development, rather than setting hard and fast rules about individual personality traits.
Defence secretary Philip Hammond, who announced the new unit, also said that "each individual case would be looked at on its merits".
"The conviction would be examined in terms of how long ago it was, how serious it was, what sort of sentence had followed. So I can't rule it out," he told Newsnight.
However, a former hacker said that the UK government's involvement with the mass surveillance unveiled by Edward Snowden had deterred him from using his cyber skills to defend the UK.
Mustafa al-Bassam, who was the youngest hacker in the Lulzsec group and is now a computer science student at King's College London, told Newsnight:
"I can understand the need for a government to protect itself, but when you go ahead and stomp on everyone's civil liberties - as we've seen with all the mass surveillance stories that have been out over the past year - I think you can rest assured that you're going to repel talented people," he said.
The MoD plans to recruit "hundreds" of computer experts as cyber reservists to protect the UK's critical computer networks and safeguard vital data. Cyber attacks were identified as a 'tier one' threat in the government's 2010 National Security Risk Assessment. This is the same category assigned to international terrorism, an international military crisis and a major accident or natural hazard requiring a national response.
The agency said that the initial part of the recruitment process will include a security-focused questionnaire, and that while the applications are open to all, candidates who have received a caution or been convicted of a crime may not be eligible to apply.