New Zealander Wood arrived at St. James' Park from Burnley for £25 million this week as Eddie Howe looked to plug a hole left up top after an injury to Wilson.
Wood is set to make his Magpies debut against Watford this weekend and, with a vital run of fixtures coming up, could cement his place in the side by the time Wilson returns to fitness.
However, Newcastle's number nine has said he isn't worried about the competition, hoping it will bring out the best in him.
The 29-year-old was speaking on The Footballer's Football Podcast with Michail Antonio.
Wilson said: "I want to make sure I'm in the best place possible for the return, especially with new competition coming through the door.
"They need to see who is King on the grass.
"It's going to be good to have new bodies in the building and add competition for places. It's going to bring out the dog in me.
"All of a sudden I'll come back with a different mentality but sometimes you have to have that little bit of a boost to get you going again."
The former AFC Bournemouth talisman went on to say he 'backed himself' to earn his spot back in the team when off the physio's table.
Wilson also recognised the club's dire need for a man up top with him out of action.
He added: "Any player he has coming in the door would say the same.
"We need players in the team who are Premier League ready right now to go and while I'm out injured you're not going to get a better striker in the bottom half of the league than Chris Wood.
"He's a different profile so I'm sure the manager has in his plans playing together, playing us one at a time."
At the start of the podcast, the two presenters also discussed recent FA Cup fixtures.
Antonio gushed about his side's triumph against Leeds United, while Wilson mused about Newcastle's shock defeat against Cambridge United.
He said: "I wasn't playing but it's always tricky when you're playing those lower league teams, them banana skins but I guess at least now we can focus on the league.
"I think for us, we're out now and we focus on the league and try and climb up the table slowly."