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The deal, which is believed to be worth in excess of £80,000-a-week plus bonuses, would potentially take the 21-year-old beyond two decades at the club he joined aged five.
Skipp, who is currently sidelined with a long-term pelvis injury, made his Spurs debut in October 2018 under Mauricio Pochettino and has made 52 appearances for the club, including 28 this season.
Last term the England Under-21 international helped Norwich to win the Championship during a season-long loan.
Skipp has not played since late January and suffered a setback earlier this month when he felt pain in his pelvis after returning to outdoor training.
His absence has frustrated head coach Antonio Conte, who has repeatedly urged the club’s medical staff to help return Skipp to fitness before the end of the season.
Tottenham travel to Brentford on Saturday as they continue their attempts to qualify for next season’s Champions League.