(Adds other airlines interested in buying TAP stake in paragraph 4 and IAG open to sell some Madrid slots to Ryanair in paragraphs 5, 6, 7)

MADRID, June 26 (Reuters) - British Airways and Iberia owner IAG may be interested in acquiring Portugal's state-owned airline TAP if conditions are right, its Chief Executive Luis Gallego said on Monday.

"The TAP operation may make sense from a strategic point of view because of the Brazilian market, they are complementary... but we have to look at the other conditions under which it is privatised," Gallego said.

The Portuguese government has said it wants to sell TAP as early as July, once the company's value is established, but intends to keep a strategic stake.

At least three major global carriers - IAG, Lufthansa , Air France-KLM - have so far shown an interest.

Separately, Gallego said IAG was open to selling some Madrid slots to Irish airline Ryanair as part of potential remedies to its acquisition of Air Europa.

IAG has agreed to buy the remaining 80% in Spanish carrier Air Europa it did not already own for 400 million euros ($435.96 million). The deal still needs antitrust clearance by the European Commission.

Ryanair said earlier this month it was keen to buy any Madrid slot the EU Commission would force IAG to sell.

($1 = 0.9175 euros) (Reporting by Corina Pons; Writing by Emma Pinedo; editing by Andrei Khalip, Inti Landauro and Susan Fenton)