Wood arrived at St. James' Park from Burnley for a fee reported to be £25 million in the January transfer market.
Eddie Howe was pressured into making an acquisition quickly at the start of the year with leading man Wilson out for a long period of time fighting an injury.
Wood had hit double figures in goals every season since 2017/18 for Burnley in the Premier League but has struggled to get going since switching to the black and white stripes.
The 30-year-old has made six appearances for Howe's side but hasn't registered a goal, despite the side's upturn in form.
Speaking on The Footballer's Football Podcast with Michail Antonio on BBC Sounds, Wilson said: "We're scoring goals and goals are coming from all different positions, but we are keeping clean sheets at the back which is something that had let us down earlier on in the season.
"I'm just rooting for Woody, being in a striker's union, to get himself off the mark as soon as possible."
Wilson's podcast co-host Antonio didn't quite believe the Newcastle man's words.
The West Ham forward said: "Don't lie! Why you lying, bruv?
"Your team is winning games, you're unbeaten in seven, your striker that's come in for you hasn't scored any goals... but you're winning games.
"You want your team to keep winning but you want to come back and get your place.
"You don't want him bagging so you've got to come in and sit on the sidelines."
Wilson was adamant that wasn't the case.
He replied: "I'm not agreeing to this. I want Woody to score goals, that's all that matters.
"I'm a Newcastle United player and I want my players to do well and be successful."
On the podcast, Wilson also spoke of the "unreal" upturn in form from his teammates.
He said: "We went away to Saudi and had some team bonding which seems to have helped.
"It's like anything really, if you get one taste of success and you get the right formula then keep applying yourselves correctly, you'll keep getting them results.
"That's what the boys have done. We're now in a position where we are looking over our shoulders, but also looking in front and who we can catch."