Fast food restaurant chain Burger King has been holding talks with private equity firms including the UK's 3i over a possible sale, according to reports.A report in the Wall Street Journal said that BK, the second largest fast food chain in the world after McDonald's, has been discussing a possible sale with possible buyers for several weeks.The talks come amid a backdrop of falling sales as customers seeking to cope with tough economic conditions. BK has also been squeezed by higher food costs, including increased beef prices in the US.Sales and profits were down in the year to June 30, the company said last week, adding that there was still uncertainty over wheat and beef prices. Commodity prices have been soaring lately, particularly for wheat, which has been impacted by hot weather in Russia and other countries.Its UK operations have bucked the declining sales trend though, with its restaurants here seeing higher sales growth, along with other markets such as Spain, Turkey and Australia.BK was owned by private equity until May 2006 when it listed on the US stock exchange. It operates more than 12,000 restaurants around the world, with 90% of these run by franchisees. The decline in sales in profits is in contrast to its larger rival. McDonald's saw profits rise by 12% in the quarter to June 30 compared with the same period the previous year as sales climbed to $5.95bn from $5.65bn. In the same period, BK's revenues fell to $623m from $630m.