The 23-year-old has been the subject of intense speculation during the summer transfer window, with suggestions he could be on his way to the Premier League.
Gunners boss Arsene Wenger is believed to admire the Bosnia and Herzegovina international, and has been linked with a bid to bring him to the Emirates Stadium ahead of the 2013/14 campaign.
Arsenal face competition for Pjanic's signature from north London rivals Tottenham, though, with Andre Villas-Boas also understood to be weighing up an attempt to lure him to White Hart Lane.
However, both clubs have been dealt a blow in their respective pursuits of the £20million-rated playmaker, after the player revealed he has no desire to leave Stadio Olimpico.
"I don't want to leave. Everyone at the club knows that," Pjanic told Roma's official website. "I've always wanted to stay here. I want to give everything to start the season well.
"I don't know about the financial situation at the club. A new contract? It doesn't happen overnight. We're talking about it. The desire is there and we'll see what happens in the future."
After arriving in Italy from Ligue 1 side Lyon in 2011, Pjanic signed a four-year deal which is now halfway through its course. And, despite receiving no information about the possibility of a new contract, he remains determined to fight for his place in Rudi Garcia's side.
"There are a number of us in that position (midfield) and whoever's on form will be in the team," he added. "The coach will find the right system. We need to do what we can to let the new signings settle.
"There are some great players who can help us to achieve success. Then it'll be up to the coach to decide who to pick."