The 26-year-old has not yet played competitively for the club after injuring his knee on their pre-season US tour, weeks after joining from RB Leipzig for £52 million.
Nkunku, last season's Bundesliga top scorer, was named in Pochettino's squad for Saturday's 2-0 win against Sheffield United as the team registered back-to-back Premier League home wins for the first time in more than a year.
He did not feature but is set to make his competitive debut on Tuesday for Pochettino's side, who struggled to break down their opponents at the weekend.
"I can tell you maybe he can play 20 minutes," the Chelsea boss said at his pre-match press conference on Monday. "How I saw him before Saturday in my mind I had one percent to two percent of doubt. That's why I didn't want to take a risk. I need to be 100 percent, then things can happen."
Chelsea have scored 28 goals in 17 league games this campaign, but they have come in bursts, with the team, 10th in the Premier League, failing to net at all in the league during September. Pochettino urged supporters to show patience with their new forward, who scored 16 goals for Leipzig last season.
"(Nkunku has trained) only in the last few weeks, after four or five months he was out," said the Argentine. "The team has evolved and the situation has changed.
"My worry is to put too much pressure on him, to say 'now has arrived the guy to make us win every single game, to change everything'. I don't believe it's going to be like that.
"He needs time to recover his fitness. Hopefully he'll play tomorrow and score three goals, then be consistent. But the most important thing is not to put too much pressure on him."
Nicolas Jackson is the top-scorer for Chelsea this season, with eight goals in all
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