Fears were mounting among some shareholders that Vodafone would be forced to overpay in a much-hyped bidding war that is going on between various suitors from across the world, the reports said, without naming any disgruntled shareholder.
When contacted, a spokesperson for Vodafone declined to comment on whether an auction-like bidding war was inflating the valuation of the target company.
The official also declined to comment on whether it has sought or plans to seek support of its shareholders for the intended acquisition.
The world's largest mobile player is pitted against Reliance Communications, which made its interest public on Thursday, as well as Essar, a minority shareholder in Hutch-Essar with a 33 per cent stake.
Hutch-Essar is reportedly being valued between $14-17 billion, but none of the players interested in the company have confirmed the valuation.
While some shareholders are opposing Vodafone's interest in Hutch-Essar, others like Standard Life Investments have been reported by British dailies as supporting the deal.
Standard Life, which has 1.7 per cent stake in Vodafone, is supporting the bid, saying the strategy of pushing into emerging markets "bodes well" for future, The Times said.
Two other newspapers - Independent and The Telegraph, also reported that Vodafone's emerging market strategy has been supported by Standard Life.