Following the roll-out of gift cards in its iOS apps over the weekend, well-placed sources have informed The Next Web that digital payments innovator Square is set to make another announcement – a partnership with British fashion house Burberry in what will be the company’s first tie-up with a luxury brand.

The partnership was first highlighted by Burberry CTO John Douglas, who tweeted that the company has installed Square’s payment readers at one of its ‘Brit’ stores in San Francisco:

Following on from Douglas’ tweet, The Next Web has learned that Burberry is conducting a payment trial in collaboration with Square in its Westfield location in San Francisco. According to sources with knowledge of the company’s plans, Square CEO Jack Dorsey is set to formally confirm the partnership and payment trial soon.

While Square was unavailable to comment on the roll-out of its Square Register terminals in the Burberry Brit store, the company has placed Burberry in its company directory.

Screen Shot 2012 12 12 at 10.35.41 730x383 Square to announce payment trial with Burberry, its first luxury brand partner

The trial makes sense for Burberry, as the company has been testing iPad apps that allow sales associates to have “personalized interactions with customers with knowledge of where they shopped, what they liked, and what they bought” since earlier this year, according to its CEO Angela Ahrendts.

For your background: earlier this year, Square secured a landmark partnership with Starbucks and will be processing all credit card payments in the coffee shop’s 7,000 stores in the United States.

The company is currently processing well over $10 billion in payments annually, an increase of $2 billion in only two months.

To date, Square has raised $341 million in funding from well-known investors and entrepreneurs in the technology industry such as Khosla Ventures, CrunchFund, Yahoo’s Marissa Mayer, Foursquare’s Dennis Crowley, Google Venture’s Kevin Rose, First Round Capital, SV Angel’s Ron Conway, Twitter co-founder Biz Stone, Shawn Fanning, Sequoia Capital, Kleiner Perkins Caufield & Byers, and more.

Those aren’t the only investors — non-tech entities have also gotten involved with Square, including Starbucks (naturally), Visa, Virgin Media’s Richard Branson, Rizvi Traverse Management, and Citi Ventures.

Also read:

The future of money: New paradigms for the checkout, banking & currency

Top image credit: Ari / Flickr