The fund invests in Accel Partners, a US venture capital firm that led the fundraising for Wonga in 2009, the report states.
A Lambeth Palace spokesperson said: “We will be asking the Assets Committee of the Church Commissioners to investigate how this has occurred and to review the holding in this pooled investment vehicle.”
Newcastle striker Papiss Cisse has agreed to wear the logo of sponsor Wonga on his shirt.
The 28-year-old Muslim had refused to display the pay-day loan company's branding on his kit because earning interest is forbidden by Islamic Law.
However, after several weeks of delicate negotiations, the Senegal international and the club have now found a solution and the player, who missed the club's pre-season training camp in Portugal as a result of his stance, will return to the fold.
The Church of England's Head of Mission and Public Affairs says the time the Archbishop of Canterbury spent in cities including Durham has influenced his decision to tackle pay-day loans companies.
Rev Dr Malcolm Brown said: "This is a man who has worked in a lot of major cities in the country - Coventry, Liverpool, Durham.
"He wasn't in Durham very long but he found out a great deal about it and that's been a major factor in the way he's approached the whole question of finance, banking and the way people work with money."
Wonga has responded to the Archbishop of Canterbury's claims that the Church of England plans to go head-to-head with pay-day lenders.
Errol Damelin, founder and Chief Executive of Wonga, said:
"The Archbishop is an exceptional individual, with our discussions ranging from the future of banking and financial services to the emerging digital society. On his ideas for competing with us, Wonga welcomes competition from any quarter that gives the consumer greater choice in effectively managing their financial affairs”
– Errol Damelin, founder and Chief Executive of Wonga
The Most Rev Justin Welby read law and history at Trinity College, Cambridge and began his career in the oil industry based in Paris and London, where he worked on West African - mainly Nigerian - and North Sea projects.
He became a group treasurer in a company called Enterprise Oil, before resigning in 1987 after 11 years in the industry to train for the Anglican priesthood.
He has also served on the parliamentary Banking Standards Commission.