Savile, who police believe may have abused up to 300 children over four decades, reportedly left an estate worth £4.3 million ($6.9 million, 5.3 million euros) when he died in October last year at the age of 84.
The scandal surrounding Savile, one of the best-known stars of British TV and radio from the 1960s until the 1980s, has dragged in several public institutions where the abuse allegedly took place, including the BBC and three hospitals.
"Given the claims raised, distribution of the estate has been put on hold," NatWest said in a statement.
The Financial Times reported that Savile's estate totalled £4.3 million, of which £3.7 million was to be held by NatWest on behalf of Savile's charitable trust.
Savile was almost as well known in Britain for his charity fundraising as for his shiny tracksuits and love of cigars, raising an estimated £40 million for various causes in his lifetime.
Lawyers representing his alleged victims are expected to sue for damages.
Police say around 300 people have come forward with abuse claims linked to Savile, which would make the eccentric entertainer one of the most predatory sex offenders in British history.
Police questioned 1970s glam rocker Gary Glitter, a convicted paedophile, on Sunday on suspicion of sexual offences, the first arrest in the widening police probe into the activities of Savile and others around him.
The BBC has has launched an inquiry led by a former judge into its own culture and practices, in a bid to find out how one of its biggest stars was able to get away with the alleged abuse for so long.