Windows were smashed and a Mercedes S600 car parked in the driveway was vandalised.
A group angry at bank executives' pay contacted a newspaper claiming to be behind the early morning attack.
Police said they were investigating these claims as part of their inquiry, adding that they took planned attacks "very seriously".
There has been widespread public and political anger over a pension payout worth about £700,000 a year to the 50-year-old former chief executive.
Sir Fred took early retirement from RBS last year after the bank needed a £20bn bailout from the government.
Last month, RBS reported that it made a loss of £24.1bn in 2008 - the largest annual loss in UK corporate history.
Windows of the stone villa have been smashed
When Sir Fred stepped down from the post in October, he rejected government pressure to accept a reduction in his package, insisting that changes to the early retirement deal he had negotiated were "not warranted".
The payout was described as "obscene" and "grotesque" by MPs and "unjustifiable and unacceptable" by Prime Minister Gordon Brown.
It is not known if anyone was in the house at the time of the attack or who reported the vandalism. ' From the BBC NEWS.
My view is that however unfair something is, mindless violence will not make it any less so.
As for the drawing, I know I can do better already! I was in such a hurry to get started that I grabbed the nearest things, a pencil and paper off the printer, instead of going to the studio. I don't like graphite because it is shiny and I prefer a paper with a bit of a tooth for drawing.