The 21-year-old, who only joined the Foxes from Manchester City five months ago, had been tipped to find first-team football elsewhere by Nigeria boss Gernot Rohr.
Puel says that Iheanacho remains a work in progress at Leicester, however, having started the striker just twice in the Premier League so far and the same number of times in the EFL Cup.
Responding to Rohr's comments, the Frenchman said: "We don't know about what the national trainer said. We will see. We have discussions with different players. For example Iheanacho is a young player, arrived this season, and he will stay with us.
"I cannot talk about details about players. It is important to have a good balance in the team and have a good game time for the players. Iheanacho is a young player, he signed this season with us and we have to develop him. I hope he can have more game time in the second half of the season.
"For Iheanacho there has been a lot of speculation. He is a young player who arrives in a good team where there is competition and he needs to keep working and improve."
Fellow Nigeria international Ahmed Musa has also been linked with a move away, but Puel refused to comment on the ongoing speculation.