By Kimberley Kao

U.K. budget airline easyJet has agreed in principle to a higher takeover offer by U.S. investment firm Castlelake, in a deal that could exceed $7 billion.

In a joint statement on Sunday, the companies said the latest proposal--the fifth from Castlelake--stands at 6.90 pounds a share. This is up from a previous proposal of 6.50 pounds a share.

The offer represents a 24% premium to easyJet's closing price on Friday and gives the airline an equity value of 5.23 billion pounds, equivalent to $6.98 billion. The valuation rises to 5.52 billion pounds on a fully diluted basis.

easyJet's board has agreed to extend the deadline for a firm offer from Castlelake to Aug. 3.

"There can be no certainty that any firm offer will be made, even if any pre-conditions are satisfied or waived," the statement said.

Castlelake would agree to a "'best endeavors' commitment in any cooperation agreement to obtain any regulatory clearances and approvals required to consummate the transaction," it added.

Minneapolis-based Castlelake, which has about $37 billion in assets and owns an aircraft-leasing business, has been courting easyJet with a series of takeover bids in recent weeks.

Shares in easyJet have gained over 40% since Castlelake made public its interest in a possible takeover, recouping its losses since the war in the Middle East began and cast a pall on airline stocks.

Write to Kimberley Kao at kimberley.kao@wsj.com