By Agence France-Presse
The Irish singer owns a stake in a Maltese company that bought the mall via a Lithuanian holding company in 2007, according to the so-called Paradise Papers leaks reported by the BBC and the Guardian newspaper.
The enterprise, in the Lithuanian city of Utena, is now under investigation for possible tax avoidance, after it allegedly avoided paying £41,500 ($54,500, EUR47,000) in local taxes using an unlawful accounting technique, they reported.
Bono -- whose real name is Paul David Hewson -- was "extremely distressed if even as a passive minority investor... anything less than exemplary was done with my name anywhere near it", he said in a statement obtained by the BBC and the Guardian.
The singer said he had been "assured by those running the company that it is fully tax compliant", they reported.
"The fact is, I welcome this reporting," he added, calling for public registries in offshore tax centres.
The revelations stem from a trove of documents leaked from a Bermuda-based law firm, Appleby, and reported by the US-based International Consortium of Investigative Journalists (ICIJ) through partner media outlets around the world.
Bono, a well-known activist in the fight against Aids in Africa, has received international recognition in recent years for anti-poverty advocacy through his "One" charitable organisation.
"I take this stuff very seriously. I have campaigned for the beneficial ownership of offshore companies to be made transparent. Indeed this is why my name is on documents rather than in a trust," he added.