Rightmove says it will “carefully consider” a third sweetened offer for the property portal from an Australian rival owned by Rupert Murdoch.

REA Group has offered the Rightmove board a bid worth 761 pence for its shares, valuing the business at £6.1bn.

REA says this is a 9.2% increase on its second bid for Rightmove on 5 September and a 39% premium on the UK firm’s undisturbed share price on 30 August, the day before the Australian firm’s interest became public.

REA says Rightmove shareholders would hold around 20% of the enlarged business.

Rightmove says: “The board will carefully consider the increased proposal, together with its financial advisers.”

This is a change from the UK board’s previous statements, which rebuffed REA’s two previous offers.

Richmond-based REA is held by News Corp, and employs almost 3,000 staff trades across Australia, Asia and the US under a series of brands, including PropTrack, realator.com and PropTiger.com.

The Australian firm says, “there are clear similarities between REA and Rightmove in terms of their leading market positions in the core residential business”.

It adds that an “enlarged group would represent a highly attractive investment opportunity for both REA and Rightmove shareholders”.

Rightmove shares lifted 1.8% to 686.2p in mid-morning trading.

AJ Bell investment director Russ Mould says: “If you want to own the market leader, you must pay a premium price and that’s exactly the situation with Rightmove.

“The fact REA has now made three different offers shows it is serious about wanting to own Rightmove. Pouncing on the business after a lacklustre period for the share price, there was always the chance REA was simply trying its luck while the target was going through a tough period.

“That no longer appears to be the case. This looks like a serious pursuit, albeit one where the bidder’s idea of fair value still doesn’t align with shareholders’ expectations.”