Malaysia can lay claim to be the center of the world's global Islamic economy, but the United Arab Emirates (UAE) is hot on its heels, according to new research.

The "State of the Global Islamic Economy Report 2018/19," commissioned by the Dubai Islamic Economy Development Centre (DIEDC) and produced by Thomson Reuters, shows a narrowing gap between the two hubs. The Islamic economy is the Muslim-majority countries that have financial sectors and economies which comply with Islamic law.

"Although Malaysia once again tops the Global Islamic Economy Indicator, the UAE ranks in first place across the remaining five sectors — halal food, halal travel, modest fashion, halal media and recreation, and halal pharmaceuticals and cosmetics — compared to three sectors in 2017/18," the research said. The report evaluates the quality of the overall Islamic economy ecosystem including social considerations relative to a country's size.

Malaysia's lead is supported by its dominant Islamic finance ecosystem, but the UAE (which consists of seven seven emirates including Abu Dhabi and Dubai) is making progress to narrow the gap, according to the man tasked with that job.

"The Islamic economy sector has grown in importance over the last few years, and the year-on-year growth has been quite significant," Abdulla Mohammed Al Awar, the CEO of the Dubai Islamic Economy Development Centre, told CNBC's "Capital Connection."

The center aims to make Dubai the global capital for the Islamic economy, and position Dubai as a leading engine of Islamic finance and a solutions provider for the halal industry.

"Ever since the launch of our strategy in 2013, we've witnessed the local growth of the Islamic economy in the Emirate of Dubai," Al Awar added.

"We did a measure of that in 2017, and realized that the contribution of the Islamic economy sectors in the Emirate of Dubai was close to 8.3 percent, which is close to $9 billion in terms of the contribution to GDP (gross domestic product), so that's significant that there is another layer of economic contribution that was in place after that vision," Al Awar said.