"Emaar Malls has submitted a bid of $800 million (736 million euros) for Souq.com in line with the strategy to align e-commerce with physical shopping," Emaar Malls said in a statement.
Amazon, which walked away from talks with Souq.com earlier this year, had offered up to $650 million (600 million euros) for the company, according to Bloomberg.
As of Monday Souq.com had not publicly responded to Emaar's offer.
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Founded in 2005, the e-commerce site emerged as the highest-valued internet company in the region last year after a funding round raised more than $275 million (250 million euros).
Investors in the site include Standard Chartered Private Equity and the International Finance Corporation, a member of the World Bank Group.
Souq.com has reported more than 1.5 million sales to customers in the Middle East and North Africa, particularly the United Arab Emirates, Saudi Arabia and Egypt.
Emaar Malls owns Dubai Mall, one of the world's largest shopping centres.
It is the retail arm of real estate giant Emaar Properties, which is the largest company listed on the Dubai Financial Market and was behind the world's tallest tower, Burj Khalifa.