Spanish outlet Sport reported that Barça officials made the approach as they search for a striker to replace Robert Lewandowski, whose contract expired this summer. Kane, 32, was one of several names on the club's wish list, along with Atlético Madrid's Julián Álvarez and Manchester United's Benjamin Sesko.
The initial response from Kane's camp was described as "cold." He is understood to be content with life in Munich and wants to remain at the Allianz Arena.
The situation is nonetheless complicated by an impasse in contract extension talks with Bayern. Kane's current deal expires in 2027, and while both parties are open to a renewal, they are at odds over the length of any new agreement.
Kane is seeking security until 2030, while Bayern are prepared to offer only two additional years. Negotiations have been put on hold until after the World Cup.
Kane had an outstanding 2025-26 season at Bayern Munich, scoring 36 goals in 31 Bundesliga appearances to claim the European Golden Shoe. He also won the DFB-Pokal before joining England's squad for the World Cup in the United States, Canada and Mexico, where he scored twice against Croatia to equal Gary Lineker's record as England's all-time leading World Cup scorer.
Should he fail to extend his contract before entering the final year of his deal, the pressure on Bayern to consider offers from rival clubs would intensify significantly.
Barcelona remain hopeful that any contractual friction could open a route to the player later in the summer, but their primary focus remains Álvarez.