The Algieran, who is 30, has become a key member of Pep Guardiola's team over the past 12 to 18 months.
He is currently on a £160,000-a-week deal, which runs out in a year and a half.
According to The Sun, Mahrez's extension is the next priority for City, after they renewed the contracts of several first team stars in the summer.
City are also hopeful of tying down England winger Raheem Sterling, who is unhappy about his game time this term.
Source: Tribalfootball
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