Home Affairs says it's agreeing a policy this week to ensure refugees coming to live in Guernsey are safe and their living arrangements are suitable and dignified.
Deputy Rob Prow says his committee is working "at pace" and the parameters of the scheme have been developed.
Once the policy is agreed, then refugees fleeing the war will be matched with locals who've offered to home them.
Home Affairs says this phased approach ensures that local volunteers are still able to take in Ukrainian refuges and that the living arrangements suit both parties. It will also ensure those newly arrived from eastern Europe can access the support they may need.
It was concern over this support, and how it might affect health, social care and education in Guernsey, that has delayed the scheme.
Deputy Prow says he recognises that many islanders want him to get it running:
"We know there is a strong desire from many in our community for this scheme to be in place as soon as possible and we expect further significant progress imminently, which will then allow us to focus on the process of matching potential sponsors, who have appropriate accommodation available, with Ukrainian beneficiaries."
Both deputy Prow and deputy Peter Ferbrache have met with the charities set up to support family members of Guernsey residents who've moved here from Ukraine. Deputy Prow says it was a useful meeting:
"I would also like to take this opportunity to thank the charity representatives, who have already done so much to support the settling in of Ukrainians already here as part of the Family Scheme, for the very productive meeting Deputy Ferbrache and I had with them last week. It was very useful and welcomed."