The group, which supplies wheels and brakes for aeroplanes, agreed a 6.3 billion pound ($8.7 billion) takeover offer from U.S.-based engineer Parker-Hannifin in early August, in the latest example of corporate America's appetite for British companies.
Days later, Meggitt said it had also been approached by U.S. aircraft components and systems maker TransDigm, at a possible 900 pence per share, higher than Parker-Hannifin's 800 pence level.
Meggitt shares traded at 819 pence in early deals on Monday.
The Takeover Panel, which overseas mergers and acquisitions in Britain, said TransDigm has until 1600 GMT on Sept. 14 to either make a firm offer or rule itself out of the running.
Meanwhile the process for Parker-Hannifin's firm offer continues, with Meggitt announcing earlier on Monday that it had published documents in relation to the offer, with a date set for a shareholder vote on Sept. 21.
Parker, which operates in the industrial and aerospace markets, has made a series of commitments to the British government on jobs and security.
Separately in the aerospace and defence sector, private equity-owned Cobham said on Monday it has agreed to buy London-listed Ultra Electronics for 2.57 billion pounds and has set out commitments to allay government concerns over national security.
On Meggitt, the Takeover Panel said its deadline would cease to apply if a third party other than TransDigm gatecrashes the party with a firm offer for Meggitt.
"Each of Meggitt, Parker and TransDigm has accepted this ruling," the regulator said in its statement.
($1 = 0.7219 pounds)
(Reporting by Sarah Young; editing by James Davey)
