The firm, which was a contender to supply 126 multi-role fighters to India, is seeking to win export customers as it closes in on providing the 160 jets ordered by UK's Ministry of Defence, according to a report in The Telegraph.
So far the Royal Air Force (RAF) has taken delivery of 129 of the twin-engine planes which, according to government data, cost 87 million pounds each.
India is almost certain to buy French company Dassault's Rafale fighter, but BAE and its partners are campaigning to win new customers in the Gulf including Kuwait and for Saudi Arabia.
BAE and its German, Italian and Spanish partners in the fighter are "aggressively campaigning to win more customers."
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Other countries targeted include Malaysia, while Belgium, Denmark and Finland have all made inquiries about the jet.
In a briefing at the Royal International Air Tattoo, in Fairford, Glos, the company, RAF and ministers said that the jet was being upgraded from a "multi-role" to a "swing role" jet, with greater capabilities that make it more attractive to potential buyers.
The Typhoon was in competition to secure an order from the Indian Air Force seeking to upgrade its outdated Russian MiGs with modern Medium Multi-Role Combat Aircraft (MMRCA).
However, during Prime Minister Narendra Modi's visit to France in April, India agreed to buy 36 Rafale fighters in fly-away conditions.
And yesterday, Defence Minister Manohar Parrikar said the Rafale combat planes and associated systems and weapons would be delivered in the same configuration as had been tested and approved by the Indian Air Force.