BERLIN (Reuters) - Shares in online food ordering firms Delivery Hero (>> Delivery Hero) and Takeaway.com (>> Takeaway.com), battling for control of the German market, jumped on Monday after the chief executive of the Dutch company raised the idea of a merger.

Shares in Delivery Hero were up 4.5 percent at 0932 GMT, while Takeaway.com rose 3.6 percent.

The online takeaway business has been booming in recent years, prompting listings of firms such as Britain's (>> Just Eat), U.S. market leader GrubHub (>> GrubHub Inc), as well as the more recent entry of Amazon (>> Amazon.com) and Uber [UBER.UL].

However, online food delivery is seen as a "winner takes all" game as most users usually only download and use one app, meaning there is only enough space in most markets for one or two major players, prompting a wave of consolidation.

Takeaway.com CEO Jitse Groen was quoted on Saturday as saying a merger with Delivery Hero could be an option.

"In each country, there can only be one supplier," Groen told German daily Tagesspiegel.

On Monday, Delivery Hero CEO Niklas Ostberg said: "We believe there will be consolidation in our industry. For Germany, we think it's unlikely in the short term."

Delivery Hero, which listed on the Frankfurt stock exchange last year, is the world's biggest food delivery platform but is battling for control of its home market with Takeaway.com and the fierce competition is weighing on profitability.

Delivery Hero has a market capitalisation of 6.1 billion euros (5.38 billion pounds), while Amsterdam-listed Takeaway.com has a market capitalisation of 2 billion euros.

Delivery Hero, in which South African e-commerce giant Naspers (>> Naspers Limited) is a big investor, last month made a placement of new shares as it sought to raise funds to expand through acquisitions.

Shares in Takeaway.com dipped earlier this month after it reported disappointing order growth in the fourth quarter. Delivery Hero reports 2017 figures on Feb. 7.

Takeaway.com says meal orders at its German unit Lieferando have outstripped those of Delivery Hero's top German brands Lieferheld and Pizza.de by 20 percent, however, Delivery Hero says it is still ahead.

(Reporting by Nadine Schimroszik; Writing by Emma Thomasson; Editing by Louise Heavens)