The venue at South Street delivers a range of services for families with children aged between 0 to 19.
But when the contract came up for tender Palfrey Community Association, which currently runs it on behalf of Walsall Council, lost out to CGL (Change, Grow, Live).
The group has since launched a petition which has received huge support in four weeks.
Council leader Sean Coughlan has had his hands tied over the situation as he is community director of Palfrey Community Association and has had to declare an interest during any discussions.
He said: "It was a proper open tender process and unfortunately our bid wasn't as good as CGL.
"We will continue run it until April 1 and we will be sitting down with CGL to make sure the transfer goes through properly."
Anna Rogozinska, who started the campaign, said: "We are all against this decision made by Walsall Council and would prefer for the centre to be locally run through Palfrey Community Association as it has done for a number of years.
"We cannot understand how a centre which has two Outstanding Ofsted reports would have a change in management especially from outsiders who may not know our community as well as the local people who provide our children with activities do.
"We would like for you to rethink your decision and keep our Children's Centre local and run by local people."
The petition is available on change.org