The mall owner, Capital Shopping Centres, has submitted a planning application to Renfrewshire Council for permission in principle to build a new mixed use development.
If approved, the work will create up to 5000 jobs.
The Evening Times revealed the plans last August.
They include a department store and additional shops at the western end of the mall and new leisure facilities.
At the proposed site, between the existing Xscape and the shopping centre, plans include an arena for ice and other sports, concerts, entertainment shows, conferences and exhibitions, a public square, improved access to the river edge and external landscaped walkways, cafes and restaurants and a 200-bed hotel.
It is hoped the plan will create 2000 construction jobs – including apprenticeships – and 3000 direct and indirect jobs in leisure and retail when the development is completed.
CSC says it will work closely with Renfrewshire Council and the Employability Partnership to ensure as many jobs opportunities as possible go to local people.
The plans also include a significant boost to public transport, with the creation of an integrated interchange for buses which would also take in the new Fastlink service, which it is hoped will extend from the Southern General Hospital, Glasgow, to Braehead and Renfrew.
Peter Beagley, regional centre director for CSC, said: "This will be one of the biggest private investment projects in Scotland for a long time.
"With planning consent, we will be creating thousands of jobs at a time of economic downturn and it will be a boost not only to Renfrewshire, but the west of Scotland economy."
No date has been set for the council to consider the plans, but Bob Davidson, chief executive of Renfrewshire Chamber Of Commerce, said they would be good news for the area.
He said: "The Chamber is pleased to hear the plans have been well received.
"The expansion plans will mean Renfrewshire will be home to one of the top shopping and entertainment destinations in the UK."
Renfrewshire Council leader Mark Macmillan added: "It's very encouraging that one of the biggest private sector investments in Scotland over the next few years is scheduled for Renfrewshire.
"The detail of this particular planning application will now be considered by councillors on the relevant policy board in due course."