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Ajose has been nominated for February's player of the month award after scoring six goals in his last four games.
Austin scored 37 goals in 65 games for Swindon and earned a move to Burnley, before later playing in the Premier League with QPR and Southampton.
"Obviously for me the next step hopefully is to prove myself in the Championship," he told BBC Points West.
"I truly believe I can score lots of goals at that level. Hopefully, the run we're on at the moment, we can sneak up in the top six and maybe we can be doing that next year."
Ajose has scored 20 goals in 30 games this season since joining from Leeds in September, equalling Austin's highest goal tally for the League One side.
"You look at people like Charlie Austin and Rickie Lambert, Jamie Vardy, these kind of players," Ajose said.
"Obviously Vardy went from League Two to the Championship and now he's on fire in the Premier League, so I don't think there's any ceiling, especially for strikers.
"If you're that kind of striker who can score goals, you can score them at any level as long as there aren't massive deficiencies in your game."
Swindon are seven points adrift of the play-off places with 12 games to play, but they have a game in hand on every team above them in the League One table.
The Robins have won four straight league games to move up to 13th in the table, having been as low as 23rd in November after a 12-match winless run.
"We're confident and we know that if we can keep this run going we're going to be right in the mix," Ajose said.
"Hopefully we can catch a few people by surprise.
"The quality we've got in the dressing room and the way we want to play, it's a lot different to any other team in the league probably bar Wigan, but I'd say we do what we do better than them."
Swindon striker Nicky Ajose wants to emulate former Robins player Charlie Austin and play at a higher level.