Aston Villa are currently looking for a new manager following the departure of Remi Garde.
Neville was sacked by Valencia earlier this week, after struggling in his first managerial job.
The former Manchester United defender won just three La Liga matches with Valencia, and he leaves the Spanish giants sitting only six points above the relegation zone.
Keown does not feel that Neville should be written off because of his poor start to management, however, and he has suggested that the Villa job could be a possibility.
"I think it would be wrong if Neville didn't get back into management somewhere, and quickly," Neville said. "Otherwise the Valencia experience will look like a waste of time. He will have learned a great deal in that short space of time and now I think he has to decide whether he wants to be a manager or a coach.
"As for the next spot? Who knows. It wouldn’t be beyond the realms of possibility that Aston Villa might consider him. But right now he is working with England and his involvement at Euro 2016 will make it difficult whichever path he takes."
Villa are currently on the hunt for a new manager, after they decided to part company with Remi Garde earlier in the week.
The French boss departed the Midlands club after a disastrous spell, which saw him win just two Premier League matches.
Villa are now planning for life in the Championship, with their relegation from the top flight looking inevitable.
The Claret and Blues are currently 12 points adrift of safety, but Sean Dyche, Steve Bruce and Nigel Pearson are regarded as more likely candidates than Neville to take over.