The Daily Star says the France left-back is demanding a three-year deal worth £120,000-a-week, plus a £6m signing-on fee and a testimonial.
So far the Gunners have offered to keep paying Sagna £60,000 a week for two more years after this season.
"The player's first option is to stay at Arsenal," said a source close to Sagna.
"He will consider signing a new three-year contract, salary £5m to £6m a season, plus signing-on fee and bonuses. It also has to include a testimonial at the end of the deal, when he would have completed 10 years at Arsenal.
"There is one more round of talks left before the season finishes.
"He is very keen to finish his career in an Arsenal shirt but wants to be rewarded for staying loyal to the club when others walked out. And he has had no pay rise since 2008."
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