The move would mark a radical shift in strategy for Microsoft, which still dominates the personal computer market but has failed to get any real traction on tablets and phones, partly because of a lack of apps.
Microsoft has found itself in a circular trap, as many developers will not build apps for Windows phones because they have so few users, and few people use the phones because there are fewer apps than on Android or Apple Inc phones.
Allowing Android apps onto its phones and tablets could be a shortcut to breaking out of that trap. Microsoft will also look at allowing apps from other platforms on its phones, said one source, opening the door to thousands of Apple iOS apps.
The sources requested anonymity because they were not authorized to speak publicly about the matter.
The strategy runs the risk of making Windows phones less attractive if they are merely seen as emulations of Android or Apple devices. But Microsoft may have no choice, according to analysts.
"Their approach recognizes that code for a mobile app can start from any of a number of sources," said Al Hilwa, an analyst at tech research firm IDC. "The only approach to succeed today is to recognize the multiple developer ecosystems out there."
Microsoft, which bought Nokia's handset business last year, currently has only 3 percent of the global smartphone market. By contrast, Android phones, led by Samsung, control 81 percent of the market and Apple 15 percent, according to Strategy Analytics.
The world's biggest software company is scheduled to release its new Windows 10 operating system this summer, which for the first time will run across PCs, tablets and phones.