The Scotsman reports that chief executive at the bank Antonio Horta-Osorio is considering offloading the insurer - and Morgan Stanley and Deutsche Bank are believed to be evaluating the situation.
It comes after speculation linked Mr Horta-Osorio with a sell-off of insurance assets as he attempts to balance his company's finances.
Selling Scottish Widows could stand to earn Lloyds between Â£5 billion and Â£7 billion if it focuses more centrally on its core retail banking services.
The newspaper observed that a possible buyer for the company could be Clive Cowdery's Resolution Group, despite the consolidator recently dismissing talk of its acquisition ambitions.
It was recently announced that Lloyds is to slash a further 325 jobs from its wholesale group operations.
The bank noted the downsizing will come as part of its integration with HBOS and sees job losses at the organisation since 2009 reach the 22,000 mark.
By Asim Shah