In a joint announcement, the two companies said there could be “no certainty at this stage” that the discussions would result in a deal.
But a merger for two of the industry’s weaker players would be attractive.
It comes a year after Nokia sold its struggling handset business to Microsoft.
Analysts and investors suggested the deal could face potential opposition from the French government, which has previously said it sees the communications industry as strategic, and is sensitive about any potential job cuts.
Nokia is valued at around €29bn, almost three times as much as Alcatel, which had a market capitalisation of €11bn based on Monday’s closing share price.
Some investors expressed scepticism over the merits of the proposed deal.