The move comes as life insurers in the UK are also having to adapt to an overhaul of taxation rules which effectively give retirees more control over their pension pots, no longer compelling them to buy annuities on retirement.
Shares in Phoenix, which makes money by buying up closed life books and running them more efficiently, rose as much as 4.8 percent to 902.5 pence after it confirmed a media report on Wednesday, before slipping back to trade at 867.5 pence by 1215 GMT (1315 BST).
The company said it was evaluating a bid for Guardian Financial, currently owned by private equity firm Cinven [CINV.UL], as one of a number of further "consolidation opportunities" in the UK closed life sector.
It has in the past paid around 70-80 percent of embedded value (EV) for acquisitions, analysts said, implying a price tag of between 1.89 billion pounds and 2.16 billion pounds for Guardian Financial, which last reported an EV of 2.7 billion pounds, similar to that of Phoenix.
EV is a standard industry measure that includes the net present value of estimated future profits from an insurance portfolio and the net asset value attributable to shareholders.
If finalised, this could be the third big deal this year in the UK life insurance market after Aviva's acquisition of Friends life and the merger of Just Retirement and Partnership Assurance.
"We view Guardian Financial as well managed and would represent a transformational deal for Phoenix ... the issue is whether Cinven would accept the level of discount implied in the current rating of Phoenix," Shore Capital analysts said in a client note.
A takeover of Guardian would bring assets worth about 18 billion pounds to Phoenix, adding to its assets under management of 52 billion pounds, according to its website.
The deal would also boost its cash generation, substantially lift its dividend and buys back assets it was forced to sell to Guardian in 2012 when it had to reduce its debts.
However, the conclusion of any talks are expected by analysts to have to await clarification from regulators on the precise impact of the European Union's new Solvency II capital adequacy rules on providers of savings products which promise certain levels of return.
"I think (Solvency II is) part of the reason Phoenix sold annuities to Guardian Assurance in the first place. So why would they want to buy it back if the Solvency II treatment is quite harsh?" Canaccord Genuity analyst Ming Zhu said.
"To get something solid done on the deal, I think, in terms of the timeline, they would really have to have more clarity on Solvency II," she said.
In addition Phoenix -- which reported a 49 percent fall in its first-half operating profit -- would have to raise debt or equity capital from the market for such a large purchase. Analyst Zhu estimated that the company has about 300 million pounds of cash for acquisitions.
Phoenix could also see some bidding competition from Swiss Re AG's closed life funds arm, Admin Re, said Sky News, which first reported on the possible deal.
($1 = 0.6450 pounds)
(Reporting by Esha Vaish in Bengaluru and Carolyn Cohn in London; Editing by Anupama Dwivedi and Greg Mahlich)
By Esha Vaish and Carolyn Cohn