The German coach was announced as Frank Lampard's successor last week and penned an 18-month deal at Stamford Bridge.
That leaves Chelsea seventh in the Premier League, six points off the top four with 17 games of the season left to go.
According to the Daily Mail, finishing in the Champions League qualification spots is a must this season if Tuchel is to earn a contract that runs beyond the end of 2021-22.
The Blues are said to have included the clause, and various other incentives, in a bid to avoid paying out large sums of compensation to managers after sacking them for underperforming.
Owner Roman Abramovich has paid around £110m to sacked managers since buying Chelsea in 2003.