The council aims to make Salford a “child friendly city” and “improve the attractiveness and safety of local neighbourhoods”.
Mr Dennett said: “I wish there was more progress made, but Swinton is not off the table, it’s one of the town’s that is an absolute priority for me moving forward.”
The council is also facing a squeezed budget, having lost millions in government spending cuts over the past decade, according to the mayor.
Mr Dennett added: “Towns are really important to the future of Salford, it isn’t all about what happens at MediaCity or close to Manchester.”
West Bromwich Building Society said they were not the owners of Swinton Square but were the lenders to the owners, who are two overseas registered companies.
“LPA receivers are appointed over the property and they have been actively managing the centre and have continued to actively engage with various heads of department at Salford council in relation to the current management of the centre and in relation to the future of the Swinton shopping centre,” a spokesperson added.
“They have maintained an open and honest dialogue with the council, which we expect to continue, but despite historic and ongoing dialogue with Salford council, the receivers have yet to receive any form of offer, or proposal from the council for the Swinton centre.”