The news comes as the district prepares to help UK-bound refugees escaping the war in Ukraine.
A serious shortage of homes has been blamed on the issue.
The council later confirmed that 38 of the 63 refugees it had agreed to take were still waiting for permanent accommodation in the district, with the Home Office responsible for putting them up in hotels in the meantime.
Last September it was reported that five families had been giving permanent accommodation shortly after arriving in Wakefield, though at that point more were still waiting in hotels.
Coun Jeffery spoke about the issue on an online Q&A session on Monday, after being asked about the council's response to the Ukraine crisis.
She said: "We had the situation (last year) with Afghanistan. The situation there is the refugees who came from Afghanistan haven't been rehoused yet.
"They're all in temporary accommodation in hotels.
"If we bring a lot of people from Ukraine, we're hoping people will take them into their homes because it's difficult to find them some accommodation.
"We haven't got an influx of empty houses waiting for people to come."
She was also critical of the government's handling of the situation, with individual refugees needing to be sponsored by people willing to offer them a bed before they can arrive here.
Coun Jeffery added: "It's a very difficult situation.
"It's not made easier that people have to have a named person to sponsor them.
"If you're fleeing a country, you're not going to sit down on your laptop, hoping someone's picked you up.
"There must be a better way.
"We're hoping there'll be some government legislation coming out over the next week to make it easier for us."
Local Democracy Reporting Service