British toy retailer Hamleys is close to finalizing a deal where it would secure roughly 30,000 square feet at 2 Herald Square, near Macy's and Victoria's Secret , a person familiar with those negotiations told CNBC, requesting anonymity because the talks are confidential. The store is expected to open in 2020, should the deal go through, said the person, cautioning talks are still ongoing between the tenant and landlord and nothing has been finalized.

Companies like Target , Walmart , Amazon and Kohl's are trying this holiday season to sell more toys to kids and their parents, but the verdict is still out on which company will best fill the void that Toys R Us left behind. Seeing a huge opportunity, one iconic, international toy retailer could soon make its first move into the U.S. with a flagship location in New York, and plans for a wider rollout of stores to follow.

Without Toys R Us, an $11 billion toy industry has been left with no clear market leader.

Hamleys has been around since 1760 when it opened its first location in England. Today, it has a flagship shop on tourist destination Regent Street in London, in addition to locations all across the Middle East, Asia and Africa. And in North America, Hamleys has three stores in Mexico.

After an opening in New York, Hamleys would look to other major markets like Los Angeles, Chicago and Miami to open stores and would consider moving into some of the more profitable malls in the country, said the person familiar with its plans.

Hamleys didn't immediately respond to CNBC's request for comment. SL Green, which owns the space at Herald Square, declined to comment.

Hamleys' opening near Herald Square in New York would follow that of FAO Schwarz, which just returned to the city with a flagship location last month.

In the U.K., Hamleys' stores are known to draw kids in for the experiences they offer. Kids can play with life-size Lego figures while employees will dress up as fictional characters to entertain shoppers, for example. This excitement in stores is what many people say the toy industry is now missing in the U.S.

"These days you have to have Amazon and e-commerce in your sideview mirror," Mark Kaplan, principal and chief operating officer at Ripco Real Estate, a New York-area brokerage firm, told CNBC. "From a consumer standpoint, if I can buy something online and it's a commodity, I will do that."

"But if the in-store experience offers something more ... where I can test out a product," that's how you win shoppers away from the internet, he said. "There's no doubt Toys R Us opened up the landscape for the next new toy concept."

As Hamleys closes in on its deal in New York, other big-box retailers are still vying to take whatever share of the market they can get.

Over this year's Black Friday weekend, the retailers that gained the most market share left from Toys R Us were Walmart (10.6 percent), Target (6.2 percent), Kohl's (3.4 percent), J.C. Penney (2.9 percent) and Costco (2.1 percent), Gordon Haskett found in partnering with Alpha Hat and analyzing the geolocation data from roughly 6,700 shoppers that visited Toys R Us during the same three-day period (from Friday to Sunday) in 2017.

But Chuck Grom, an analyst at Gordon Haskett, said the majority, or nearly 59 percent, of last year's Toys R Us shoppers during Black Friday weekend simply "vanished," or didn't make purchases at other retailers' bricks-and-mortar locations.

"Consumers appear to have gone to fewer stores and/or did more shopping online," Grom said.

The Commercial Observer first reported last week on Hamleys nearing a deal in New York.