Valiant and BeKB both confirmed the talks in brief statements after the Inside Paradeplatz financial news website reported that Valiant had offered itself for sale to BeKB.
Citing two unnamed sources close to Valiant, the website said Valiant wanted BeKB to pay 124 francs per share or almost 2 billion Swiss francs ($2.16 billion), adding that another option could be for it to take a strategic stake.
Valiant said it would not comment further beyond confirming the talks about a possible merger as part of an evaluation of strategic options. BeKB also declined to comment further.
Valiant shares extended earlier gains after the confirmation of talks and traded up 5.9 percent at 100 francs at 6:52 a.m. EDT. BeKB shares were down 0.4 percent at 256 francs.
Founded in 1997 and based in Bern, Valiant, whose biggest shareholders include Zuercher Kantonalbank and Norges Bank Investment Management, has about 1,000 staff and more than 400,000 clients.
BeKB was founded in 1834 and has about 1,450 staff and 500,000 customers largely in the cantons of Bern and Solothurn.
The Valiant stock has been under pressure since Swiss financial market regulator FINMA ruled in April that the bank had artificially propped up the price of its shares in 2010, infringing its duty to ensure proper business conduct.
Reporting by Emma Thomasson; Editing by Mike Nesbit