The 22-year-old, who recently shot to the top of the charts with These Words, lost the computer earlier this month.
It contained new material as well as uncut work from her debut album, Unwritten, and had been stored inside her suitcase, The Sun reported.
Police said: "We can confirm a female has reported the alleged theft of a laptop computer at Heathrow airport.
"The theft allegedly happened on September 2 and was reported to Heathrow police on September 5.
"No arrests have been made and inquiries are continuing."
Natasha, whose brother Daniel is also a successful singer, hit the charts in May with her first single, called Single.
Social bookmarking allows you to save and categorise a personal collection of bookmarks and share them with others. This is different to using your own browser bookmarks which are available within your web browser.
Use the links on the left to share this page on the social bookmarking site of your choice.
Read more about social bookmarking at: Wikipedia - Social Bookmarking