LONDON/DUBLIN (Reuters) - Aer Lingus (>> Aer Lingus Group Plc) has rejected a takeover approach from the owner of British Airways (>> International Consolidated Airlines Grp), which is keen to gain control of the Irish airline's slots at London's Heathrow Airport.

Shares in Aer Lingus (>> Aer Lingus Group Plc) surged as much as 20 percent on Thursday after the Financial Times reported that British Airways-owner International Consolidated Airlines Group (IAG) (>> International Consolidated Airlines Grp) was considering a takeover bid.

IAG later confirmed its approach, but gave no details. "There can be no certainty that any further proposal or offer will be forthcoming," it said in a statement.

Aer Lingus said the approach undervalued its business, but also did not give details. At 1615 GMT, its shares were up 8.8 percent at 1.98 euros, giving it a market value of about 1.06 billion euros ($1.30 billion).

IAG shares were 4.2 percent higher at 462.5 pence.

Buying Aer Lingus would give British Airways more take off and landing slots at London's Heathrow Airport, a key hub for profitable long-haul routes but which is operating at close to capacity, preventing the airline from adding more flights.

IAG chief executive Willie Walsh knows Aer Lingus well. He started his career as a pilot there and was the former national carrier's chief executive between 2001 and 2005.

But any acquisition of Aer Lingus would need the backing of budget Irish carrier Ryanair (>> Ryanair Holdings plc), which owns a 29.9 percent stake in Aer Lingus after three failed takeover attempts, and the Irish government which owns 25 percent of the carrier.

Ryanair declined to comment on Thursday. The airline is currently appealing an order by Britain's Competition and Markets Authority to cut its stake in Aer Lingus to 5 percent.

Ryanair Chief Executive Michael O'Leary has said he does not plan a fourth bid for Aer Lingus, which Ryanair had planned to use as a premium-economy brand to compete with easyJet.

However, Ryanair has indicated it may take its appeal to European courts, which could freeze its stake for over a year.

Cantor analyst Robin Byde said it would make sense for IAG to look to expand at Heathrow, where it currently has about a 51 percent share, compared with Aer Lingus's 3 percent. However, he added Ryanair's position could prove a sticking point.

"Ryanair would negotiate hard," Byde said.

Ryanair has repeatedly said it has not had a serious offer for its Aer Lingus stake. But the expected resolution for Aer Lingus of a large funding hole in a staff pension scheme in the coming weeks might increase interest in the Irish airline.

Ireland's department of transport has said the government would be open to selling its Aer Lingus stake when the price and market conditions were right.

($1 = 0.8150 euros)

(Additional reporting by Sudip Kar-Gupta; Editing by Mark Potter)

By Sarah Young and Conor Humphries