An Australian property company majority-owned by Rupert Murdoch’s News Corp has said it is considering a takeover bid for Rightmove, the British property website.

REA Group said it was considering a possible cash and share offer for Rightmove, but that it had yet to have any discussions with the company, in statements to the Australian and UK stock markets on Monday.

Shares in Rightmove surged by 27% to £7.08 on Monday, up from £5.55 on Friday night, making it the top riser on the FTSE 100 and giving it a market value of £5.8bn.

Rightmove is the UK’s leading property portal market, and estate agents across Britain use the site to advertise properties for sale and rent.

However, Rightmove’s position is expected to come under pressure after the American property company CoStar bought rival UK site OnTheMarket from a consortium of high street agents that had hoped to win back control of the market from Rightmove and the second biggest portal, Zoopla.

A formal bid would raise the prospect of another FTSE 100 company leaving the London Stock Exchange, after several years of warnings that UK-listed companies are being undervalued by investors. Travel company Tui shifted its main listing to Frankfurt in February, while cybersecurity company Darktrace has agreed a takeover deal with a US investor.

REA did not say how much it was considering offering for Rightmove, but the British company was valued at £4.4bn on Friday before the potential bid was revealed. The company said there was no certainty of making a formal offer. It has until 5pm on 30 September to do so under UK takeover rules or walk away.

REA was founded in 1995 in a garage in Melbourne. After floating in 1999, its value soared during the dotcom bubble before crashing. It owns a number of property websites in Australia, including realestate.com.au, property.com.au and the data company Proptrack. It also has several brands in India, and realtor.com in the US. The company has previously tried to expand into the UK, but it sold that operation to Zoopla in 2009.

The Murdochs first bought a stake in 2001. Their company, News Corp, owns 61% of REA’s shares, with no other shareholder owning more than 2%, according to S&P Global Market Intelligence.

REA has risen to a stock market value of A$29bn (£15bn), more than News Corp at A$24bn. That prompted activist investor Starboard Value to put pressure on News Corp last year to sell REA to realise its value. The campaign came a month after Rupert Murdoch announced his retirement from direct leadership of his media empire.

Rightmove was founded in 2000 by four corporate estate agencies: Countrywide, Connells, Halifax and Royal and Sun Alliance. It was initially free to list properties, with charging introduced in 2002.

Rightmove listed its shares on the London Stock Exchange in 2006. Its biggest shareholders are the Los Angeles investment manager Kayne Anderson Rudnick, with 20%, and the British investment manager Lindsell Train, with 6.6%.

REA said it saw “clear similarities” with Rightmove’s “leading market positions in the core residential business, continued expansion and innovation of offerings across adjacent segments, leading audience share and strong brand awareness, as well as highly aligned cultural values”.

It said the deal would be a “highly attractive investment opportunity for both REA and Rightmove shareholders”.

Jessica Pok, an analyst at investment bank Peel Hunt, said the company had been undervalued “due to the negative sentiment on the UK housing market and concerns over competitive threats from CoStar/OnTheMarket”.

She said the company was attractive because of the stability of the core business of advertising homes, plus “growth opportunities in other revenue streams such as mortgages, commercial real estate and rental” under its chief executive, Johan Svanström.

However, Giles Thorne, an analyst at investment bank Jefferies said REA’s interest appeared to be more a financial than a strategic move, because there was “little in the way of cross-border synergies” given that housing markets can be very different.

Thorne said the main benefit for Rightmove offered by REA would be “strategic and execution insights to what is already a tightly managed business”, and REA’s experience in mortgages and commercial property, both of which Rightmove has targeted as growth areas.

Rightmove has been approached for comment.