Presidential candidate Xavier Vilajoana has already initiated contact over a potential move for the England striker, should he win next month’s election at the Spanish club.
Vilajoana - one of four confirmed candidates in the presidential race - has pledged to pursue a deal for the striker, if elected.
Kane, 32, has scored 41 goals for Bayern this season and remains one of the most prolific forwards in world football.
Barcelona are expected to part ways with Robert Lewandowski when his contract expires at the end of the campaign. At present, a move to MLS side Chicago Fire FC appears to be a strong possibility for the Polish international.
And Kane could be next in line to lead the Barca front line - if the pieces fall into place.
Addressing the situation in an interview with ESPN, Vilajoana said: “What we’re missing is a striker - a centre-forward capable of linking up play, but also a killer in the box…
“There is one. In fact, 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.”
The words are a warning to Bayern, who have already managed to fend off interest from Saudi Arabia, where lucrative offers were made in an attempt to lure him away from European football.
But while Kane had no interest in that move, Barcelona would represent a far more serious challenge for Bayern to contend with.
Kane continues to hold big ambitions in the game. He wants to fill up his trophy cabinet in the final years of his career, and the chance to move to Spain would be appealing.
Bayern’s ideal scenario is to secure Kane’s future by agreeing a contract extension before the end of the season - and that remains their objective.
His current deal runs to 2027, and talks about a new agreement have been ongoing throughout this season. But Barca are, perhaps, the only club that could truly turn Kane’s head.
A significant payday has never been his primary motivation, as demonstrated by his lack of interest in a move to Saudi Arabia.
Yet to join one of the very biggest clubs in the world would bring new opportunity and trophy potential.
For now, Bayern are in pursuit of their own treble and hope they can convince Kane to stay.
But transfer discussions are likely to become a hot topic as this season hits the latter stages.
