AFC Bournemouth have signed Christian Atsu from Chelsea on a season-long loan deal.
Midfielder Miguel Pallardo has signed a new one-year deal with newly-promoted Hearts while Danny Wilson leaves.
The 22-year-old New Zealand international looked set for a move away from the King Power Stadium after dropping down the pecking order with the summer arrival of Argentinian forward Leonardo Ulloa.
But after Leicester's 2-2 result in their Premier League opener at home to Everton on Saturday, Wood said: “I sat down with the gaffer on Monday and told him that I wanted to stay and fight for my place.
“I’ve got to get my head down and work hard.”
Wood earned Leicester a point on their return to the Premier League with a goal four minutes from time, the second time in the match the Foxes had come back from a goal down.
Wood was on as replacement for Ulloa who had earlier scored Leicester's first equaliser.
He added: “It's nice to be off the mark and it was a great result for us on the opening day. It was a good point in the end.
“There are a lot of positives to take and things to learn. We’ll build on this. We showed a great performance.”