Ronald Koeman's future in Catalonia remains far from secure, although the Dutchman has retained the faith of Joan Laporta for the time being, in spite of his side's ninth-placed standing in the La Liga table.
Barca have previously been linked with a move for Klopp, but the Liverpool boss has frequently outlined his plans to take a break when his Reds deal expires in the summer of 2024.
However, Sport claims that Klopp is still Barcelona's 'number one candidate' to succeed Koeman, but the Blaugrana accept that any attempts to prise the German away from Liverpool will be futile.
The report adds that Barca will aim to put a lucrative package together to tempt Klopp into making the move to Camp Nou, which has been described as an 'almost impossible' dream.
Klopp has now taken charge of 330 games in all competitions for Liverpool and chalked up his 200th Reds win during Sunday's 5-0 thrashing of Manchester United.