The 22-year-old has been linked with a move away from the Foxes following the arrival of Leonardo Ulloa earlier this summer.
However, after scoring a late equaliser for Leicester in Saturday's 2-2 draw with Everton, Wood admitted that he is keen to stay at the King Power Stadium.
"I sat down with the gaffer on Monday and told him that I wanted to stay and fight for my place," he is quoted as saying by Sky Sports News. "I've got to get my head down and work hard."
Leicester return to action next Saturday when they travel to Chelsea in the Premier League.