The Zurich-based reinsurance specialist is believed to be the current favorite to secure the deal, with Deutsche Bank also being considered as a potential buyer, AFX News reports.
Speaking to the news agency, Collins Stewart analyst Tim Young said that such an acquisition in the UK insurance market would be an ideal proposition for Swiss Re.
"The fact that Swiss Re would be in a deal like this makes sense because they are trying to build a UK closed life business," he was quoted as saying.
"[Swiss Re] has a very strong closed life business track record in the US."
Germany's Deutsche Bank is also expected to be interested in taking over the company, with many investment banks keen to access the lucrative annuities market.
GE Life is reportedly on the market for around Â£340 million.