The Times reported that in May, Sefton Council in Merseyside saved £1.6 million in stamp duty by buying the New Strand shopping centre in Bootle for £32.5 million via a company registered in Luxembourg.
It also bought insurance against the possibility that HM Revenue and Customs might chase it for payment, it was reported.
And in July, Warrington Council agreed to pay more than £200 million for Birchwood Park, a business centre in Cheshire, via an offshore company, saving almost £10.5 million in stamp duty, according to the newspaper.
There is no suggestion that the arrangements used are illegal.
But Mr Corbyn has long criticised legal tax avoidance, and responding to the Paradise Papers leaks this week, called for the Queen’s finances to be investigated as part of a wider inquiry into the revelations.
The Labour leader also indicated the monarch should apologise if her private estate invested £10 million of her personal fortune offshore to avoid paying tax in Britain.
Sefton Council told The Times: “We paid all the tax due and will continue to do so. The council bought the company that owned the asset as this was the corporate structure that was marketed for sale.
“We acquired the shopping centre primarily to deliver a new revenue stream to help pay for vital services that have been reduced as a result of government cuts. The purchase also supports regeneration in Bootle.”
Warrington Council, which still holds Birchwood Park in an offshore company according to the newspaper, said: “The only tax not being paid is a one-off payment of stamp duty land tax.
“This position was discussed in detail and followed extensive due diligence and external advice to the council.
“To complete the acquisition in a timely manner the council agreed to leave the business offshore as trying to complete the deal and bring it onshore would have delayed the purchase.”
A Labour Party spokesman said: “The Labour Party is committed to changing the current tax environment and to tackling tax avoidance.”