Brookfield has prevailed over other investment firms in an auction that Data4's majority owner, Axa Investment Managers, held for the company, the sources said on Friday.
If negotiations and financing arrangements are concluded successfully, a deal could be announced as early as next week, the sources added.
The sources cautioned that there remained a chance that no deal would be completed and asked not to be identified because the matter is confidential.
Brookfield declined to comment, while representatives for Data4 and AXA Investments, a division of French insurer AXA (AXAF.PA), did not immediately respond to requests for comment.
Headquartered in Paris, Data4 operates at least 25 data centers across France, Italy, Spain and Luxembourg, according to its website.