Enterprise zones, like the one already in operation on the former HMS Daedalus site in Lee-on-the-Solent, have low business rates and relaxed planning rules to encourage companies to set up there.
Speaking at an event in London today, Southampton City Council leader Richard Williams told Mr Clegg: "Things are not all rosy in the Southampton area at the moment."
He said: "The question is, given the difficulties that we're experiencing at the moment, particularly around the Ford plant at Southampton, is there opportunity...to include that area in a new enterprise zone?"
Mr Clegg said the Ford announcement had been "very bad news", and said it was up to local leaders to put forward a case for new powers for the area.
He was speaking as the government offered to hand over swathes of new powers and funding to council leaders in 20 areas of the country, including Southampton and Portsmouth.
As reported in the Echo, leaders of the two councils will present a bid to the government asking for specific powers to boost growth in the Solent region. This could include control over buses or tax-raising powers.
Mr Clegg said: "The deals are unlocking the huge potential of our cities so they can go for growth.