The New Zealand international striker was a target for Championship club Wolves during this week, but the two clubs were unable to agree a deal and Pearson is adamant he wants to stay.
And Wood picked the perfect time to showcase his commitment to the Leicester cause as he came off the bench to score a later equaliser in a 2-2 draw with Everton on Saturday on the opening day of the Premier League season.
"He is staying," said Pearson.
"In terms of that story [the potential transfer to Wolves], we've not fanned the fire.
"It's been a story that's gathered speed but he's staying here.
"I've spoken to him on a couple of occasions this week and he's very happy to fight for his place. As far as I'm concerned, I draw a line under it there, I'm pleased to have him here.
"And I am very pleased he was able to play his part in securing our first point in the Premier League."
