Helloworld has tentatively offered 90 cents per share, a 19 per cent premium to Webjet's closing share price on Tuesday.
Webjet Group shares were up 13.9 per cent to 86 cents in Wednesday morning trading, while Helloworld shares were up 2.0 per cent to $1.78.
"A combination of Webjet and Helloworld would create a powerful business proposition in the dynamic travel bookings industry," Helloworld Travel chief executive Andrew Burnes said.
Helloworld's brands include Helloworld Travel franchise outlets Magellan Travel, Express Travel Group, Express Tickets, Phil Hoffman Travel, eta and Viva Holidays.
The company has already amassed a 17.3 per cent shareholding in Webjet, whose board has agreed to provide Helloworld an opportunity to conduct due diligence.
Separately, Webjet said on Wednesday it delivered a statutory net profit after tax of $6.2 million for the six months to September 30, up 51 per cent from a year ago.
Webjet's underlying earnings before interest, tax, depreciation and amortisation fell nine per cent to $14.4 million, with revenue down marginally to $67.9 million.
Webjet's bookings fell eight per cent to 724,000, with domestic bookings dropping 10 per cent and international bookings rising four per cent.
They represented a total transaction volume of $726 million, down three per cent from a year ago.
Webjet said the results reflected a leisure travel market impacted by cost-of-living pressures, tension in the Middle East, disruptions from US tariffs and elevated domestic airfares following Rex's exit from major city routes.
"Our results for the period were broadly in line with expectations, demonstrating the resilience of our business, despite experiencing challenging market conditions," said chief executive Katrina Barry.
The company announced an inaugural interim dividend of two cents per share, a payout of 100 per cent of its underlying net profit after tax.
Webjet said it had begun relaunching its brand with a redesigned website and significant spend on social media websites.
Webjet Group was demerged in 2024 from the company now known as Web Travel Group, whose operations include WebBeds, a business-to-business accommodation supplier and wholesaler.
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