Chelsea defender Ben Chilwell (AFP)
The left-back limped out of Tuesday's 4-0 Champions League win against Juventus following a challenge from France international Adrien Rabiot.
But Tuchel said on Friday that the 24-year-old may be able to avoid surgery, allowing him to play again sooner than expected, which would be a huge boost for the Premier League leaders.
"Ben has a partial injury of his ACL (anterior cruciate ligament) and the decision is to treat it conservatively," Tuchel said.
"And the next six weeks will tell the story actually if he makes it and if he will be fully available after the six weeks, or if he needs surgery after that.
"Right now I only care about the six weeks -- we are very positive because the first reaction of his body is very positive."
Marcos Alonso is likely to deputise for Chilwell during the hectic December schedule, starting with Manchester United's visit to Stamford Bridge on Sunday.
Chilwell had won back his place from Alonso after largely being consigned to the bench at the start of the season following a frustrating lack of playing time with England at the postponed Euro 2020.
He has returned to his best recently, scoring four times in five games for Chelsea and England in October.
Although surgery remains a possibility depending on Chilwell's recovery pathway, Tuchel said the defender remained upbeat.
"We need to talk about it again in six weeks, maybe we don't need to talk about it because everything is fine," Tuchel said.
"This is the best case. It does not help if we start now speaking about worst cases, because there is also a best-case scenario."
Chelsea are also likely to be without France midfielder N'Golo Kante against United due to a minor knee issue.
(For more sports news and updates, follow Ahram Online Sports on Twitter at @AO_Sports and on Facebook at AhramOnlineSports.)