Reports in Spain have suggested Juve is ready to try to bring the Brazil international to Turin, possibly as a replacement for Miralem Pjanic, whose future appears unclear.
Mundo Deportivo claimed on Tuesday (AEDT) that Barca has given permission for Juve to speak to Arthur as the Serie A leader can offer contract terms well beyond the means of the Blaugrana, whose players have already agreed to a 70 per cent pay cut during the coronavirus pandemic.
However, Arthur, who joined the LaLiga champions from Gremio in 2018 in a deal potentially worth €39million, sees his future in Catalonia.
In a statement sent to Mundo Deportivo, he said: "There will always be speculation but, sincerely, my idea is very clear. The only option that interests me is to continue at Barcelona.
"I'm very secure and relaxed. I feel really well here and, plus, I'm grateful to the club and technical staff for their confidence. This is yet another reason to be totally clear that my only desire is to continue.
"The supposed interest of great clubs is always a compliment for anyone and a positive sign, but my mind is only on playing here for many years.
"Barca is where I have always wanted to be and I want to be Blaugrana for a long time, beyond any other question. Every day, I feel more comfortable and well here, in the team, at the club and in the city. Also, I love both the people and the culture here [and] I feel a lot of support from the fans.
"I'm concentrating 100 per cent on working and coming back to play when possible because I'm really eager to keep improving here and to fight for more trophies."
Arthur, 23, has made 23 appearances in all competitions for Barca this season despite problems with injuries.