Michael Fallon, speaking on board a British destroyer anchored in Doha port, said he had held discussions on a possible sale with Qatari officials within the past week.
He added that the deal had not been killed off by a Qatari decision to buy 24 Rafale jets from France.
"It's definitely still on the table," said Fallon, who is in Qatar to attend the three-day Dimdex defence and security fair.
"It's something I have discussed with the new Qatari defence minister, (Khalid bin Mohammad) Al-Attiyah.
Asked if the French deal could scupper the prospective British sale, Fallon responded: "No".
"Qatar is one of our most important regional partners," added Fallon.
Britain's BAE Systems builds the Typhoon in cooperation with European aircraft maker Airbus and Italian defence firm Finmeccanica.
Britain has long sought to sell Typhoons to Qatar and is in the closing stages of wrapping up a deal to sell the jets to Kuwait.
Two other countries in the Gulf -- Saudi Arabia and Oman -- have also purchased Typhoon jets.
Around 10 of its planes have been used in the ongoing Saudi-led military operations in Yemen.
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