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AT&T and Verizon Communications confirmed Monday that they are in talks with Netflix for a deal that would increase the download speeds of the video service's movies and TV shows for their broadband Internet customers.

Their acknowledgement comes two days after Netflix said it has agreed pay Comcast to have the largest U.S. broadband Internet provider connect directly to Netflix's servers in transmitting movies and TV shows, an arrangement that would remove key data traffic bottlenecks.

Like many content providers in heavy demand, Netflix uses third-party content distributors to help distribute its movies to Internet service providers, which in turn stream them to their customers.

Netflix also operates its own set of servers in data centers. And in their deal, Comcast is now bypassing these third-party distributors to connect directly to Netflix's network. AT&T and Verizon are pursuing similar arrangements.

"We're in discussions with Netflix to establish a more direct connection between our networks, similar to agreements we have with others, so that AT&T broadband customers who use Netflix can enjoy an even better video experience," AT&T said in a statement.

Verizon Communications CEO Lowell McAdam told CNBC on Monday that his company has been talking with Netflix for about a year and expects a deal. "I'm not here to pre-announce a deal," he said. "But it's in both parties' interest."