Investors have written to BHP Billiton
The newspaper said shareholders, which it did not name, have asked for commitments from the group's boards that they use their strong balance sheets to return cash to investors.
It said the investors have moved to pre-empt another spate of deals in the mining sector that analysts and investment bankers have predicted.
The paper said some shareholders have told the companies they were prepared to vote down the re-election of key board members if they did not agree to the commitments.
BHP, the world's largest miner, scrapped a hostile offer for Canadian fertilizer maker Potash Corp
Over the last five years the company has returned $25.7 billion to shareholders in dividends and buybacks.
The Sunday Telegraph cited one of BHP's top 10 shareholders as saying: Frankly, after the Potash debacle we are not too enamored with BHP's bid ambitions.
Rio is in talks with Africa-focused coal miner Riversdale
The newspaper cited one of Rio's top 10 shareholders as saying: There is a danger with Rio that Riversdale is just the start.
BHP and Rio both declined to comment.
(Reporting by James Davey; Editing by Dan Lalor)