Denise Jeffery said she'd been made aware of claims the local authority was planning to purchase the shopping centre, which counts Morrisons and Primark among its big anchor name retailers and is under private management.
Speaking at a full council meeting on Wednesday however, Coun Jeffery said there was no prospect of that happening.
Coun Jeffery said: "I understand there's some rumours going round that we're buying the Ridings Shopping Centre. That's not the case.
"It's not our role to buy into shopping centres.
"In the 1980s we did actually own The Ridings. We designed it, built it and owned it, but that's not the case now.
"We're looking after our communities and businesses but we're certainly not into buying shopping centres at a time like this."
Local Democracy Reporting Service