South African shareholders of the mining company Anglo American have signalled they are open to a revised takeover offer from BHP, despite warnings from South African politicians and unions that a deal could be bad for the country.

Investors, which collectively own more than 15% of the London-listed mining company, told the Financial Times that they were not opposed in principle to an acquisition by its Australian rival but said an improved and less complex offer would be needed.

It comes after the ruling African National Congress has been publicly critical of BHP’s move, with its mining minister, Gwede Mantashe, saying South Africa’s experience with BHP “was not positive”.

Last month, Anglo rejected a £31bn takeover offer from the Australian company, in what would have been the biggest deal in the mining sector for a decade.

At the time, the board unanimously rejected the offer, saying it “significantly undervalued” the company and its future prospects.

As part of the BHP proposal, Anglo’s South African platinum and iron ore businesses – Amplats and Kumba – would be excluded from the deal, which the board deemed “highly unattractive”.

However, several local investors have now told the FT that they would be open to a revised offer, but stressed this would need to be at a higher price because of BHP’s desire to spin off the South African parts of the business.

Dawid Heyl, a fund manager at Ninety One, which owns 2.1% of Anglo, said a deal along the lines proposed could be struck but the price would have to be substantially higher.

He said: “It would be easier, though, if BHP were to come back with a higher and simpler offer, which removes the conditionality of getting rid of Amplats and Kumba, which would make it trickier.”

Karl Leinberger, the chief investment officer at Coronation Fund Managers, which owns 1.2% of Anglo, said that it would “definitely” consider a deal but BHP would have to pay more if it wanted to exclude the South African businesses.

This is at odds with the mining minister Mantashe, who has publicly stated that he is against the takeover.

Speaking after the rejection of the first offer last month, Mantashe said BHP’s merger with the South African miner Billiton in 2001, “never did much for South Africa”.

South Africa’s government-owned Public Investment Company is Anglo’s largest stakeholder and owns a 7% stake in the company.

The Congress of South African Trade Unions, which includes the National Union of Mineworkers, has also urged local shareholders to reject a BHP bid, saying a deal would not be in the national interest.

BHP now has until 22 May to make a formal offer for Anglo American under UK merger and acquisition rules. There is speculation that other global mining companies could also enter the race, with Rio Tinto and Glencore also reported to be eyeing up bids.