Vilajoana, one of four candidates standing in the club's presidential election on March 15, spoke openly about his admiration for the England captain. Kane, 32, remains under contract at FC Bayern Munich until 2027 after joining from Tottenham Hotspur in 2023.
"We've already made some contact, and I think he's a player who would be a great fit, pending his contractual situation: it's Harry Kane," Vilajoana said.
He added: "Kane is a centre forward who would fit in perfectly with our style of play. He's capable of dropping back to link up with his team-mates, but he can also play as a pure No 9, a killer, a finisher. He brings mobility and performs well when teams sit deep. He would add a lot of value to Barcelona's game."
Vilajoana also claimed the striker would be open to the move. "I also know that he likes Barcelona. There are very few players who don't like Barcelona. So it's a matter of talking about it."
Kane's impact in Germany has been outstanding, with 126 goals in 131 appearances for Bayern across all competitions. Whether he would seek a new challenge in La Liga or consider a return to the Premier League remains uncertain.
Vilajoana, who previously served on the board under Joan Laporta, Sandro Rosell and Josep Maria Bartomeu, is viewed as an outsider compared to current favourite Laporta. Other candidates include Victor Font and sports economist Marc Ciria.
His transfer stance could also affect Marcus Rashford. Barcelona reportedly hold an option to make Rashford's loan permanent for 26 million pounds.
"I believe you should always look in-house first," Vilajoana explained. "Then look outside depending on the characteristics of the players you have. The president puts things on the table, alternatives are considered and a decision is made.
"What I am clear on is that if signing Rashford is considered the best sporting decision, the money will be there."
With the election looming, Barcelona's future direction - and potential marquee signings - now hangs in the balance.
Paris Saint-Germain have decided to end their legal battle with Kylian Mbappe after confirming they will not appeal a French labour court ruling ordering the club to pay up to 61 million euros in unpaid wages and bonuses.
Michael Olise will step onto the pitch this weekend for Bayern Munich with more than just three points on his mind.
Borussia Dortmund head to RB Leipzig on Saturday knowing the stakes could hardly be higher in the Bundesliga title race.
Real Madrid have received a much‑needed boost as defender Eder Militao edges closer to returning from a serious hamstring injury that has kept him out since early December.
