Town councillors are unhappy at the shortage of parking spaces around the building, which is leased by five businesses, including the .Knutsford Guardian.
Macclesfield Borough Council recently rejected plans to extend parking to the grassy area to the left of the building because it threatened existing trees.
But Clr Bert Grange argued that extra parking could be provided around the trees.
"Every car park in Jersey is full of trees," he said. "They are left there to keep cars cool.
"This is exactly the same refusal we received in 1990 from Macclesfield and it does not address the situation. They need to live in the now."
But Brian Hillaby, principal administrative cfficer at Macclesfield, said the trees were protected in a conservation area.
"A car park would be likely to adversely affect the attractive setting of the building, which is listed," he said.
He suggested visitors staying longer than a few minutes should use the public car park near Booth's supermarket.
"It may be necessary that some means of enforcement may have to be introduced to secure this," he said.
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