Businesses and residents say the town centre has been hit by falling trade and gridlocked roads since major works started around Market Place last month.
Now Labour-run Sandwell Council has vowed to resolve the issue "as quickly as possible" and revealed that free parking was being considered, along with a number of other options.
The issue has become the subject of a political row ahead of this week's local elections, with Labour councillors warning there will be "no traders left" unless the authority takes action, while Tory candidates have slammed the council for "poor decisions and a lack of strategic management".
Council leader Kerrie Carmichael said she had been contacted by local councillors over the matter and acknowledged that parking in the area "was an issue".
Councillor Carmichael added: "Resolving this quickly is important to me and I am currently gathering the information necessary and will consider free parking along with any other options that are available as soon as I can."
Conservative local election candidates Marc Lucock (Wednesbury North) and Vijay Gaddu (Wednesbury South) have urged the council to take "immediate action" to bring in free parking.
Mr Lucock said: "The residents of Wednesbury are being impacted by the poor decisions and lack of strategic management by Sandwell Council."
Last week Labour councillors in Wednesbury North wrote to the authority's chief executive, Kim Bromley-Derry, saying the works had already had a "massive impact" on trade in the town.
"Could you please find a solution to rectify these issues otherwise we will have no traders left in the town when the development is completed," the letter said.
The work, which is set to last until late autumn, will see a multi-use event space created on Market Place, as well as the relocation of the open air market and new cycling and walking developments.
It means Market Place will be closed between Union Street and Spring Head until July 29, while further closures will take place in October.