Pulisic is a doubt for Saturday's Premier League trip to Southampton, and although the 22-year-old has also recently missed Chelsea's victory at Sheffield United due to personal reasons, a lack of game time has fuelled speculation he could leave the club this summer.
However, when asked at a news conference whether the forward still had a future at Stamford Bridge, Tuchel replied: "Yes, today, clearly yes, but it is not only my point of view. We have to see. For me, clearly yes because Chelsea bought Christian for a reason, for his quality, for his potential, and it is our job to bring out the best in him.
"He proved in many weeks that he has the level to be a Chelsea regular player, to have a big impact in this club. It's a challenge now to hold this level, to improve and to maintain the level and keep improving."
Pulisic, who has a contract until 2024, has struggled with persistent injury problems since arriving at Chelsea in the summer of 2019 but particularly after a hamstring injury suffered in last August's FA Cup final defeat to Arsenal.
Former Chelsea head coach Frank Lampard revealed the club were exploring specific training programmes amid fears Pulisic was struggling to cope with the rigours of regular first-team football.
Although Tuchel did not necessarily share that view, he said Pulisic is unlikely to be risked to avoid another "cycle" of fitness problems.
"We are not concerned, we are not worried, but the physical, medical department is on that," he added. "Now we have little issues in the calf. He stopped training yesterday before it becomes an injury.
"So I would not say it is an injury; at the moment it is risk management to not be injured. That relies on his history of having injuries, so we do not want to enter the same cycle.
"It is sometimes like this, and the main thing for Christian is to stay positive, keep the head up and, like I said before, be ready because he can have a big impact when he starts and he can have a big, big impact when he comes off the bench with his intensity.
"There are absolutely no decisions made for the summer. There is simply no time for that at the moment, and this is not the moment now. There is today no need to think about it."
Thiago Silva has not recovered from a thigh problem and will miss the game against Southampton, but Tammy Abraham was expected to train on Friday afternoon despite limping off in Monday's 2-0 win over Newcastle with an ankle problem. Kai Havertz is also fit after shaking off a knock.