Capital Shopping Centres, part-owned by John Whittaker, has submitted plans for a £180m, 325,000 sq ft extension to its Lakeside shopping centre in Essex.
The extra space will increase its size to 1.725m sq ft and give it 40 more shops, making it bigger than the Trafford Centre, Bluewater in Kent and Westfield London.
Only Westfield Stratford City, in east London, and Gateshead Metrocentre would be larger.
Peel Holdings' founder John Whittaker has around 25% of CSC and was made chairman earlier in the year.
He took a stake in the business after it agreed a £1.6bn all-share deal to acquire the Trafford Centre in January. Whittaker has continued to buy shares in the FTSE 100 company.
If the plans are approved CSC says it could begin construction in 2013 and complete the project by 2016.