Barnes has five goals for the club this season, while Wood also has the same number. Wood joined the club in the summer from Leeds United.
Both players are now fit for the run in, and Barnes is hoping the competition will spur them on to score more and get Burnley up into the top six in the league.
"You want to score as many goals as you can. I go out every week trying to score," he said to the Lancashire Telegraph.
"We have been going with one up front but with the competition up there we are a good group of strikers. There's no bitterness. Everyone wants each other to do well."