Di Canio has been tipped to succeed Brian McDermott, who was sacked by the Royals on Monday, in what would be his first management job in the English top-flight.
The Italian enjoyed great success at Swindon, guiding them to promotion to League One on his debut season at the club.
He then put the Robins on course for back-to-back promotions this term but stepped down as manager last month after a fall-out with the club's board.
Di Canio, who has also been linked with a West Ham move as a replacement for Sam Allardyce, feels he has proved himself capable of managing at the next level.
He said: "Now that I've proved that I have skills as a manager, I can be manager at a different level.
"My story as a manager is not a very long story (but) I've proved I'm a top manager in League Two and League One.
"Obviously someone has some doubt but it's their opinion. Someone is sceptical but that is normal, especially with me."
He added: "I believe I am at a stage now where I am a Premier League or Championship manager.
"I have already proven my ability in League Two and League One, where there are many arrogant and average players, and I was able to turn their mentality and help them become better footballers.
"You can imagine if I had the chance to do the same at the top level."