The Netherlands international is expected to rejoin his team-mates at the end of November.
Xavi suffered an anterior cruciate ligament (ACL) injury during Tottenham's 1-0 victory over Wolves in April. The injury ruled him out of the remaining matches of the season as Spurs successfully battled to avoid relegation.
ACL injuries typically require around nine months of rehabilitation, but the 22-year-old has made excellent progress and is ahead of schedule. He could return to contact training just seven months after suffering the injury, raising hopes of an earlier comeback.
His potential return would be a welcome boost for head coach Roberto De Zerbi, who will be keen to have the attacking midfielder available again. Xavi could even return to competitive action several weeks before the expected nine-month recovery period ends in January.
The 52 million pound signing will also provide competition for James Maddison in the No 10 role. Xavi scored five goals in 41 appearances during his first season in north London, showing his quality against Brentford, Manchester City and Borussia Dortmund despite an inconsistent campaign.
The playmaker had to adapt to three different head coaches during a difficult season for Tottenham. Maddison has also experienced a lengthy recovery from an ACL injury, having returned earlier this year and scored on his first Spurs start in 536 days during a 3-1 victory over Coventry last month.
That win sparked a three-match winning run for Tottenham, who will look to maintain their momentum when they travel to Leeds United on Saturday. De Zerbi will also welcome back Rodrigo Bentancur after the midfielder completed his suspension following his red card in the 1-1 draw against Manchester United.