The French financial regulator is at the head office of Airbus in Toulouse, as trouble at its parent company EADS shows no sign of easing.
Mr Forgeard was asked to resign but refused, a newspaper report said.
Among those under scrutiny are former Airbus head and co-chief executive of parent company EADS, Noel Forgeard.
He made 2.5m euros ($3.1m; £1.7m) selling EADS shares, weeks before it emerged the A380 was facing delays.
In another blow, Airbus is facing the possible loss of orders worth more than $5bn, according to reports.
International Lease Finance Corporation has warned it may cancel its contacts for the A380 superjumbo and its planned smaller cousin, the A350, Bloomberg says.
ILFC chief executive Steven Udvar-Hazy said that it would be on "safe ground" to cancel the order for the plane, which has up to a seven-month delay because of problems with the wiring system.
Airlines are now calling for compensation over the extra wait. The delays are expected to reduce the firm's annual earnings by 500m euros ($630m; £340m) between 2007 and 2010.
News of delays and impact on profits prompted EADS shares to fall 26% last week, and sparked the allegations of insider dealing against Mr Forgeard.
France's financial markets authorities are pursuing their investigation, which is also looking at the timing of the decision of other shareholders to reduce their stake in EADS.
Opposition politicians in France have called for Mr Forgeard's position at the head of the firm to be reviewed.
The board met on Monday to discuss what it has admitted is a "crisis" at EADS extending beyond Airbus.
According to unconfirmed industry sources, co-chairmen Arnaud Lagardere and Manfred Bishchoff, Mr Forgeard and fellow chief executive Tom Enders were all present.
EADS said there would be discussions of how to avoid future delays to its aircraft, but issued no official comment after the meeting.
Internal divisions are causing difficulties for the Franco-German group, with reports that changes in senior management could be imminent.
And German newspaper Handelsblatt reported that German shareholders of EADS had asked Mr Forgeard to resign, but he refused.
EADS "firmly denied" the report.
Mr Forgeard insists he sold the shares before he knew of delays to the plane and did nothing wrong.
He has said he was "shocked" by the claims he had profited from insider knowledge when he, three of his children and two other executives sold shares before the A380 announcement was made.
Pressure is growing on the French government - which owns 15% of EADS - to intervene.
"The question I am asking the prime minister is whether today Mr Forgeard can stay at the head of the EADS group?" Francois Hollande, the Socialist Party leader, said.