While the Germany international is being linked with clubs across Europe, Don Balon says Arsenal are showing the most concrete interest.
Real and Barca are also keen, particularly the Catalans.
Barca management recognise they need a player of Goretzka's 'organisational' qualities as they seek to reinvigorate their midfield.
The midfielder's current deal expires in June, with speculation in Germany suggesting a 'secret' pre-contract with Bayern Munich has already been settled.
However, in Spain they insist Goretzka remains available, though Real and Barca are falling behind Arsenal in the race for his signature.