Manufacturer Dassault Aviation is also in talks aimed at supplying 16 of the multirole combat jets to Malaysia and has resumed discussions over potential fighter sales to the United Arab Emirates, the source said.
"The discussions (with Qatar) are at the final stage," the source said, asking not to be identified because of the sensitivity of the discussions.
Dassault Aviation declined to comment.
Analysts say the French company was boosted this week by a long-awaited first export deal for the Rafale withEgypt, but is likely to face intense competition for further sales as European, US and Russian rivals step up export campaigns.
The UAE publicly rebuffed an offer to supply 60 Rafale jets in 2011, calling the proposal "uncompetitive and unworkable".
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