Sources familiar with the matter were quoted by Efinancialnews.com as saying that the proposed acquisition would be strategic fit for the lender.
Financial as well as other terms of the transaction have not been disclosed, while SWIP and RBC declined to comment.
A part of Lloyds Banking Group, SWIP managed £146.66bn worth of funds, an array of assets, including equities, fixed income, real estate and cash, behalf of its diverse client base as of 31 March 2013.
Lloyds was forced to accept a £20bn state bailout due to takeover of HBOS at the height of the 2008 financial crisis, and the bank is offloading its various operations to boost its financial position.
RBC Wealth Management had acquired fixed-income specialist BlueBay for $1.51bn in October 2010.
Other firms like Aberdeen Asset Management and L&G were reported to have also placed their bids for SWIP.
