"People keep debating about who is the king of New York. ... Hey LeBron, yes, you really want to be king of New York? Come and prove it. I'll see you July 1st, brother. Good luck," Kanter said.
James can opt out of the final year of his contract with the Cleveland Cavaliers this summer.
The Knicks would need to shed significant salary to have enough cap space to sign James to a max contract. They probably would be a long shot in any James courtship even if they had the requisite cap space.
Part of the salary shedding to create the cap space for James likely would have to include Kanter declining his $18.6 million player option. Kanter has said he's considering not picking up his player option and signing a multiyear contract with a lower annual value.
The "king of New York" reference in Kanter's video alludes to a declaration James made in an Instagram post after a Cavs victory over the Knicks at Madison Square Garden.
Kanter expressed a strong dislike for James after the game and in the wake of the Instagram post.
"I don't care who you are. What do you call yourself, 'King,' 'Queen,' 'Princess,' whatever you are," Kanter said. "We're going to fight. Nobody out there is going to punk us."
Kanter also said Knicks big man Kristaps Porzingis already held the title of king of New York.
Kanter's video Monday isn't the first instance of public courtship between New York and James.
A billboard near Madison Square Garden posted last month also played off the "king of New York" phrase, challenging James to sign with the Knicks as a free agent with the statement "King of New York? Prove it" and the hashtag #KingJamesNYC18.
Billboards in Akron, Ohio (touting the Cavaliers), Los Angeles (pitching the Lakers), Cleveland (selling the 76ers) and Portland, Oregon (promoting the Trail Blazers) also have been commissioned in the past several months.