The 27-year-old, who has two years left on his current contract at the San Siro, has been linked with a return to his native Brazil.
"I'm not thinking about going back to Brazil at the moment, I want to stay at Inter for the duration of my contract," he told the club's official website.
"If we then decide we want to renew it, that'd be great. I like Italian football even though I'm well aware of how difficult it is. I could have gone to play in Spain, but neither the team nor the contract was as attractive a prospect as coming here.
"When Inter came calling I immediately said to Santos that I wanted to come here and I'd like to stay here in Italy as long as I'm wanted."
Jonathan joined the Nerazzuri from Santos in July 2011.