EasyJet, which resolved a dispute with Stelios over the easyJet brand license in 2010, said on Monday that it was ready to act should rights established under previous agreements between him and the airline be infringed.
Relations between Stelios, whose family owns about 38 percent of easyJet, and the company looked to be improving on Friday when Stelios dropped a request for an extraordinary shareholder meeting to remove a board member.
He backed down a day after easyJet moved to return GBP£190 million to shareholders.
Luton, southern England-based easyJet said Stelios had alleged that the company has breached the terms of an agreement the two had over the brand. EasyJet said it rejects the claims.
Under the agreement, which according to easyJet, Stelios has said is no longer in force, Stelios agreed not to use his own name or a derivation of it to brand any other airline within Europe for five years.
A spokesman for Stelios declined to comment on the nature of the new airline or on the status of any agreements between him and easyJet.
A website dedicated to Fastjet was displaying a single red page without click through options and the words: "Fastjet.com by Stelios. Coming soon!"