The Georgian-born star - who spent six years of her childhood living in Belfast - is among more than 1,600 people, including celebrities, doctors and judges, who put money into the Liberty scheme, according to The Times.
Around £1.2 billion is said to have been put into the scheme from 2005 until 2009.
Melua, 29, is reported to have put £850,000 into Liberty, but a spokesman said the singer went on to settle her tax in full with HM Revenue and Customs when it was brought to her attention.
He added: "At the suggestion of her accountants at the time, Ms Melua participated in the Liberty tax planning venture back in 2008 and declared this to HMRC.
"When HMRC stated they were reviewing the scheme, she paid the tax to HMRC in full. Accordingly, HMRC are not out of pocket and she has not avoided any tax liability."
Involvement in "aggressive" tax avoidance schemes has already led to criticism of other stars, including Take That's Gary Barlow.
He faces a hefty tax bill for his involvement in another scheme, Icebreaker, which was styled as a music industry investment scheme, but was successfully challenged in court in May.
Liberty faces a similar challenge, scheduled for next year.
Last week Melua received an honorary degree from Queen's University, Belfast.
Accepting the DLit (Mus) for services to music from the academic institution, she said: "It was a complete surprise and really unexpected to be awarded this honorary degree and I am so delighted.
"I consider Belfast a city very close to my heart and to be recognised in this way in the field of music is phenomenal."