Kane sat out the Europa League victory over Fiorentina on Thursday night after breaking his nose against Crystal Palace in the FA Cup last weekend.
The striker underwent an operation on Wednesday and then took part in light training on both Thursday and Friday in a bid to prove his fitness for this weekend's match at White Hart Lane.
Tottenham will be cautious while Kane remains in discomfort but the forward could wear a face mask if it means he can play and help his team's title charge.
Pochettino said on Wednesday he expected Kane to return to action against Swansea but, speaking after the win against Fiorentina, the Spurs head coach was more circumspect.
"We need to assess him day by day," Pochettino said.
"On Thursday he was on the training ground, he ran, he made some exercises and we are happy with the way he is.
"We will see
We hope he will be available for Sunday."
Tottenham proved themselves capable of coping without Kane as they scored three goals against La Viola to make the Europa League last 16, but Pochettino will want his top scorer back ahead of a testing run of fixtures.
Swansea are the first of three opponents in six days for Spurs, with West Ham and Arsenal to follow, while Manchester United, Liverpool and two legs against Borussia Dortmund are also to come in the next six weeks.
Sitting two points behind Leicester, victory this weekend could see Tottenham go top of the table but Pochettino is determined to keep his players' feet on the ground.
"Our mentality is always next game," Pochettino said.
"The players are very excited to play again after two weeks away from the Premier League
We are in a position in the table where the motivation is big
"We need to explain nothing to them
We don't need to motivate them
Only we need to be sure we arrive in a good condition to compete
"It is important for us to keep winning games in the Premier League, it is an exciting period for us
We need to rest and try to give our best on Sunday."
Source : PA
Source: PA