Nokia shares fell up to 6 percent following the news, closing the day around 3.6 percent down. Shares of Alcatel-Lucent rocketed, ending the day more than 16 percent higher.
In a joint statement, the companies said a potential merger would take the form of a public exchange offer by Nokia for the French company.
Urging caution, the statement added: "There could be no certainty at this point that these discussions will result in any agreement or transaction."
It is unclear whether Nokia, which is a backbone of the Finnish economy, would acquire all of Alcatel-Lucent's assets, or just its wireless business.