Villa narrowly avoided relegation from the English top flight in the recently concluded 2014-15 campaign, with boss Tim Sherwood steadying the ship after taking charge of the team in February.
The Villans also reached the final of the FA Cup, but they went down 4-0 to North London outfit Arsenal at London’s Wembley Stadium on Saturday evening.
Redknapp believes that the Villa fans need to be realistic about their ambition in the coming years, but suggests that the team can end up in the top 10 next season.
“They are not going to challenge for top seven and Europa League for quite a while and the fans have to accept that,” the 68-year-old wrote in The Sun.
“Sherwood has kept them up, he’s taken them to a Cup final and he’s brought a bit of the feelgood factor back to Villa Park,” added Redknapp.
“That’s a great starting point and I do expect to see them finish a few places higher next season. Top ten would be a great achievement.”
Villa have a good team, and in Sherwood they have a manager who knows how to get the best out of players.
If the former Tottenham boss is allowed to make the signings he wants to in the summer transfer window, then the Villans should be able to compete for a top-10 finish.
It will not be easy for Villa to do so as there are a number of good teams in the Premier League, but they should give it a go.