Such a deal would give a massive boost to Aberdeen's asset base, by potentially adding the £145.8 billion managed by SWIP, which is currently owned by Lloyds Banking Group, to the £201.7 million that is under Aberdeen's control.
This could make it the largest stockmarket-listed fund manager in Europe.
But reports of its interest comes less than six months after finance director Bill Rattray said Aberdeen was "unlikely" to look at SWIP.
There are also other institutions with deep pockets understood to be looking at SWIP, including the Australian investment bank Macquarie, the Royal Bank of Canada, and French bank Natixis.
Aberdeen has grown steadily by acquisition in recent years, including snapping up a large asset management operation from Credit Suisse and other businesses from Royal Bank of Scotland and SVG Advisers.
A spokeswoman for SWIP said: "We are not commenting."
Aberdeen Asset Management's spokesman also declined to comment.
Antonio Horta-Osorio, chief executive of Lloyds, is seeking to strengthen the bank's balance sheet by selling assets to rebuild it after its 2008 taxpayer bail-out.
As Lloyds TSB the bank purchased Scottish Widows, which has a life-insurance business and the SWIP fund-management operation, for £7.3 billion in 2000.
SWIP's investment offering was overhauled two years ago when it axed 27 posts and moved to quantitative investment strategies.