Gavron, speaking at the MIPIM property festival in Cannes on the French Riviera last week, said the centre could be used to recruit foreign workers.
She said that if foreign workers could be employed within the government's guidelines they ought to be recruited.
She told Building: "I am very, very aware about the skills shortage gripping the construction industry in the South-east, and hopefully the London Development Agency's centre could help counter that."
Ray Pearse, managing director of Development Security Project, a developer, warned that contractors must be prepared for a skills shortage.
Pearse, who also spoke at MipiM, said firms must ensure that they had supply chains in place as soon as possible in the life of a project.
He said: "Due to the large amount of projects starting in the capital, contractors need to make sure they have subcontractors in place to complete jobs."
Pearse singled out the curtainwalling sector as a particular area of concern.
Airports operator BAA said in January that it planned to build three training centres for the workers at the £2.5bn Heathrow Terminal 5 project in west London.
At its peak the T5 project is set to employ nearly 5000 workers and will put a huge strain on labour resources in the capital.