The Goodison Park club have enjoyed a fine start to the 2012-13 campaign and currently sit three points behind third-placed Tottenham with a game in hand over the north London club.
And while the 49-year-old coach admits his Belgian star may still leave, he suggests finishing in the top four would give the club a much-needed financial boost and enable him to realise his ambitions.
"I would really hope Fellaini will stay if we were in the Champions League," Moyes told reporters.
"Of course, he might still go for the money on offer somewhere else, but at least he wouldn't be going for the Champions League.
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"I agree with Arsene Wenger that finishing in the top four is the equivalent of winning a trophy - even if you don't get to parade silverware."
Fellaini is suspended for Sunday's visit of Chelsea, who along with Manchester United have been interested in Everton's prized asset - and Moyes says European football would help him to prevent his best players from leaving.
"I think Everton fans would definitely swap what we have got here for what Chelsea have got - because all fans want to see their team winning things.
"I don't know whether every financial problem would be solved just by qualifying. But, for me, it would have an absolutely massive impact in terms of keeping the players I have and bringing in new faces.
"I would hope that if we made the Champions League, I would get an awful lot more money to spend on players for at least a couple of years. I think it would enable us to keep our progress going in the right direction."
Moyes is looking forward to the next round of television deals which will bring more money in to Premier League clubs, but suggests the club need a new backer in order to continue their momentum.
"To really transform the club, to make things really go through the roof, we would probably need a new owner. But what worries me is that, just to keep the progress going, we need more money.
"There's a big pay cheque coming for all Premier League clubs next year because of the new television deal. But to have Champions League money as well would be a big lift. It could really change what happens.
"It is going to be tough and we are probably big outsiders because Arsenal have been very consistent in qualifying and Tottenham have finished fourth twice in recent seasons.
"Having said that, we need to have the dream."