The 'It's Always Sunny in Philadelphia' actor and fellow Hollywood star Ryan Reynolds have enjoyed huge success since buying the Welsh club in 2020 and has set his sights on the pinnacle of the game after the Red Dragons secured a historic third consecutive promotion to reach the Championship.
McElhenney told the 'AwayDays' YouTube channel: "That's what we're going for. So, of course our goal is to get to the Premier League. And then it's to win the Premier League. Then, you're in European football and why not go out and be the best football team in the world."
Wrexham are now just one division away from the Premier League but the club's chief executive Humphrey Ker expects the Championship to be a big leap for the team, although he insists that the club won't "overstretch" themselves to remain competitive.
He told talkSPORT: "We've felt that each year that we've gone up but the jump to the Championship is massive because you have a top third of temporarily-embarrassed Premier League clubs who have their parachute payments or their wealth of international footballers who have come down from the Premier League recently or they've come to the Championship for big money.
"It's incredibly important for us – we've spoke about this since day one and that's sustainability.
"It's about making sure we don’t endanger everything that we've created here by overstretching ourselves."
Ker explained that Wrexham will be making the most of their hit documentary series 'Welcome to Wrexham' and their Hollywood connections to compete in the second tier.
He said: "We'll be doing everything in our power to leverage the documentary and the interest in Wrexham to bring in funding from the outside, but sort of supercharged and make sure that we compete and stay relevant in the Championship.
"The ambition for the guys is that they want to get to the Premier League. That's the plan and that's going to cost a huge amount of money."