Swiss Life shares were up 7 percent to 154.80 Swiss francs ($152.25) in afternoon trading on the Zurich exchange.
French business Web site WanSquare, which is owned by Le Figaro daily, cited unnamed Swiss banking sources to the effect that Allianz is preparing to make a bid for Swiss Life.
Neither Swiss Life nor Allianz would comment on the report.
Analysts said rumors of a possible takeover appear to be behind the recent rise in the value of Swiss Life shares, which have rallied more than 15 percent in a week.
"The current rise in stock value isn't the result of some change in Swiss Life's fundamentals," said Stefan Schuermann at Zuerich-based Bank Vontobel.
He added that there was "an industry logic" to Allianz reducing costs by combining operations with Swiss Life, as both have a strong presence in France, Switzerland and Germany.
"A merger is more probable than a year ago because Allianz has got some money in its coffers again and Swiss Life is still undervalued," said Schuermann.
Allianz shares were down 1.2 percent at euro87.00 ($126.25) in Frankfurt against a slight upward market trend.