Members of the British Phonographic Industry (BPI) want to prove the site, which offers downloads for as little as five pence, is illegal.
They were given the go-ahead to sue the company last week, and say proceedings will be issued in Russia this week.
The operators of allofmp3.com deny the recording industry's claims that their site is not licensed to sell music.
"We have maintained all along that this site is illegal and that the operator of the site is breaking UK law by making sound recordings available to UK-based customers without the permission of copyright owners.
"Now we will have the opportunity to demonstrate in the UK courts the illegality of this site."
Allofmp3.com is the UK's second most popular download site, accounting for 14% of downloads, a survey has said.
The website says it is licensed by the Russian Multimedia and Internet Society (Roms) and the Rightholders Federation for Collective Copyright Management of Works Used Interactively (Fair).
But the International Federation of the Phonographic Industry (IFPI) says the Roms licence is not legitimate and it would not cover consumers in other countries even if it was.
The BPI revealed it intended to take the owners of allofmp3.com to court at a hearing of the Parliamentary Culture Media & Sport Select Committee last month. It is not planning to sue users of the site.
Copyright lawyers say that, even if the BPI obtains a verdict that the website is illegal, it might have "enormous practical difficulties" enforcing the ruling in Moscow.
Taken from BBC NEWS.