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.
Analysts at Credit Suisse and Citi concurred that purchasing Alcatel-Lucent's (ASU) wireless unit would be a wise strategic move for Nokia (NSN), because of the former's presence in the U.S.
"We believe Alcatel's and Nokia's wireless businesses are a great strategic fit since ALU is as strong in the U.S. as NSN is in Europe and Japan; both have strong positions in China," said Citi in a research note on Tuesday.
Credit Suisse rated stock the of both Nokia and Alcatel-Lucent as "outperform" on Monday, and said a fair value for the French company's wireless business would be 2-2.5 billion euros ($2.1-2.7 billion).
"We believe that such a potential deal would allow Nokia to significantly improve its presence in the U.S. with AT&T and Verizon (where Ericsson and Alcatel-Lucent are key suppliers)," the Swiss bank said in a research note.
Combining two major companies would provide an industrial powerhouse in Europe, but could potentially threaten jobs.
However, French Economy Minister Emmanuel Macron announced on Tuesday that the deal would involve no job cuts in France and that the combined group planned to base research and development operations in his country, according to Reuters.
This followed a meeting at the French Elysee between the chief executives of Nokia and Alcatel-Lucent and French President Francois Hollande on Tuesday.
"It's a good move for Alcatel-Lucent because it is a move for the future, because we are building, with this tie-up, a new conquest for Alcatel-Lucent, which was a company in great difficulty two years ago," Macron said, according to Reuters.