David Moyes' side currently sit second in the Premier League after recording 13 points from their opening six games and are on course to challenge for a spot in Europe.
Howard has revealed that the Toffees have discussed their end-of-season target and, although he admits that sealing a place in the Champions League next term would be tricky, the American claims that the club have the potential to achieve that goal.
"The Champions League is a real, viable option for us. Very difficult, but it is viable," the long-serving goalkeeper told Sky Sports News.
|4/1||Everton are 4/1 with William Hill to finish in the Premier League's top four
Two stand-out performers so far for Everton have been Marouane Fellaini and Leighton Baines and, while the duo have been linked with moves away from Goodison Park, Howard is adamant that the club need to keep hold of their influential players.
"The one thing I hang my hat on is that our manager will dig his heels in and if you are going to pluck our best players you will have to pay a high price," he stated.
"He has also shown that if he gets the right money in the transfer window from those sales that he buys very well, but we do not want to lose Marouane Fellaini or Leighton Baines or any of our top players."
The 33-year-old claims that the current crop of players at Goodison Park is the best he played with since arriving at the club in 2007.
"This is my seventh season. I think it is the best squad we have had, in terms of quality from top to bottom," Howard enthused.
"You'd have to ask the manager his opinion on that but I get the feeling from being around the guys in training and in matches that it is the most talented squad we have had.
"Does that give us the best chance? Maybe, because our grit and determination is always there and that is an Everton trait. Maybe this could be our year."