Councillor Denise Jeffery said she hoped restrictions in place in neighbouring Kirklees, Bradford and Calderdale would not be imposed on the district by the government.
But both she and one of Wakefield's most senior police officers have suggested for the first time that there is a strong chance the area could become part of a West Yorkshire-wide lockdown.
The rate of new infections in Wakefield has climbed steadily in recent weeks after a drop at the end of last month and is classed as an "area of concern" by the government.
Figures in neighbouring Leeds have also risen sharply.
Councillor Jeffery and District Commander Mark McManus, of West Yorkshire Police, made the comments at a local Covid recovery board meeting last week.
A recording of the meeting, which was released by the local authority on Tuesday, showed public figures from across the district discuss the prospect.
DC McManus told the meeting: "I don't think any of us were expecting the other three areas to go into lockdown.
"I know Public Health nationally weren't recommending that but the Cabinet Office took that option.
"I think it came a bit out of the blue to the three districts.
"Hopefully we shouldn't (go into lockdown), but I think it's something we're probably on the verge of."
In response, Coun Jeffery said: "Let's hope not. I think we've got to realise that it is a possibility, but let's hope not."
Almost 200 new cases of Covid have been confirmed across the district since the start of the month. The total number since the start of the pandemic has now passed 2,000 in the last fortnight.
Earlier, Steve Turnbull, from Wakefield's public health team, had been asked if there was a prospect of the district being "sucked into a West Yorkshire lockdown".
In response, he said: "At the current levels, I'd suspect not.
"Bradford and Calderdale have high rates and then there's Kirklees to a lesser extent.
"If those start to fall week on week, then I think the risk of a West Yorkshire lockdown will recede, particularly if we and Leeds can carry on as we are we'll probably avoid it."
However Mr Turnbull later added that the figures meant he was "a little more concerned than he had been in previous weeks".
Coun Jeffery said: "We'll just have to keep our eye on this situation, but it's very concerning."
Bradford recorded 33 new cases during a 24 hour period at the beginning of this week. Calderdale and Kirklees also reported further increases in cases over the same timeframe.
Under the restrictions, people in those areas cannot visit another home or garden, unless it belongs to someone in their support bubble.
Some non-essential businesses, including skate rinks and casinos also remain closed.
Local Democracy Reporting Service