Rodgers and his Leicester City team matched a Premier League record by annihilating a poor Southampton side 9-0 at St Mary’s Stadium on Friday night.
The Foxes moved ahead of Guardiola’s Manchester City into second-place in the Premier League after their ruthless display against the Saints.
Rodgers helped Swansea City gain promotion to the English top-flight and was only unfortunate not to win the Premier League in 2013-14 season with Liverpool.
The 46-year-old is currently with Leicester City after his successful stint with the Scottish champions Celtic, where he won two league titles.
According to Neville, the Northern Irish coach can be successful at the Etihad stadium with his attacking football philosophy.
"I think if you look at what he achieved at Liverpool and then Celtic and now what he is doing at Leicester, we always talk about international coaches having philosophies and values, but he improves teams and plays great football," said Neville on Sky Sports .
"He is quite innovative and he does seem to be a great coach, the players enjoy working with him, and I'm asking the question now, why wouldn't he be seen as a coach of one of the big clubs?"
"You look at Manchester City changing to Pep Guardiola and you probably won't see Brendan Rodgers' name linked with that job because people at the club will be thinking, maybe, someone else."
"But why not? If you look at what he's done in terms of the football he plays and the improvement he has on players on the pitch.”
