Vilajoana will present his ticket today as he competes in next month's Barca presidential election.
Vilajoana posted a photo montage of Bayern striker Kane in a Barcelona jersey on social media, accompanied by a direct question: "Should we sign Harry Kane?"
Later, the former Barca executive confirmed that they are already working on that possibility.
Before today's presentation, Vilajoana said in a media release: "La Masia has always been my priority. I always say that the first thing we must do is provide our youth academy with the necessary resources and give them their first opportunity, to put them through their paces.
"Only when we don't have the talent at home should Barça be able to go to the market and attract the best talent. Like Harry Kane: a talented, team-oriented, and goal-scoring player. We are working on it."