The firm, Castlelake, publicly declared last month its interest in buying the carrier, which flies mostly across Europe.
It said on Monday that it was now appealing directly to EasyJet shareholders to consider the "merits" of its latest proposal.
Under UK takeover rules, Castlelake has until Friday to table a formal bid or walk away for six months.
EasyJet's board on Monday repeated that it considered the bid "highly opportunistic" given that its share price had fallen and its losses increased after the Middle East war sent jet fuel costs rocketing.
It said in a statement that it "remains highly confident in EasyJet's strategy and its ability to deliver attractive long-term value for shareholders".
Castlelake's third proposal offered £6.25 per EasyJet share, a premium of about 59 percent compared to the share price in late May before it disclosed its takeover interest.
On Monday, EasyJet's share price was up 3.4 percent at £5.21.
"The market doesn't believe Castlelake will succeed, given how the shares... (are) significantly below the latest bid," Dan Coatsworth, head of markets at AJ Bell, said.
