Bruce Willis is eyeing a legal bid to ensure he can pass on his iTunes library to his children when he dies, according to the Daily Mail.

The Die Hard star is concerned that his extensive music collection will revert to Apple ownership on his demise and is looking into ways that might allow his three daughters, Rumer, Scout and Tallulah, to legitimately inherit it. His lawyers are currently said to be looking at the possibility of setting up "family trusts" to act as legal holders of the downloaded music, but Willis is also prepared to consider taking Apple to court over the issue.

"Lots of people will be surprised on learning all those tracks and books they have bought over the years don't actually belong to them," solicitor Chris Walton told the Mail. "It's only natural you would want to pass them on to a loved one. The law will catch up, but ideally Apple and the like will update their policies and work out the best solution for their customers."

Willis is also considering supporting legal action currently underway in five US states to give people more rights to share music they have purchased. The actor, a keen music lover and musician, who had a UK No 2 hit in 1987 with his cover version of the Drifters' Under the Boardwalk, reportedly owns thousands of hours' worth of music on various iPods.

• This article was amended on 4 September 2012 to add a link to a subsequent story which reports that Willis's wife has denied on Twitter that he is considering any such legal moves.