The painting has fascinated viewers ever since it was exhibited in the Louvre, Paris, in 1838.
Since then, its fame has been linked to the rise in the international reputation of Spanish Renaissance artist El Greco as its creator, yet the painting presents a conundrum, researchers said.
Direct, informal portraits of Early Modern women are extremely rare and probably unique in a Spanish context.
This has led some modern scholars to propose a number of new possibilities regarding who painted it, when, and who the painting features.
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The project will explore questions of artistic technique, attribution and identity, using scientific analysis as well as research methods involving the history of dress, society and collecting, researchers said.
It will attempt to unpack the complex history and significance of the unique painting, and provide a fuller understanding of who painted it, who it might represent and when it was created, they said.
"The fascinating history of the fame of 'The Lady in a Fur Wrap' and its impact on modern art and even film is likewise being studied," said Macartney.
The technical examination phase of the research is currently getting under way using the latest scientific techniques.
"Although there is no guarantee of definitive results through technical analysis we will at the very least learn much more about how this most enigmatic portrait was painted and the relationship of its materials and methods of creation to those of other important pictures in this and other collections," said Mark Richter from University of Glasgow.
Through this collaborative and comparative approach, greater understanding of the context of portraiture and artistic practice in this period in Spain generally will be enhanced.