Everton legend Neville Southall thinks the club could be forced down the Premier League table by the spending power of their rivals.
Southall, rated one of the best goalkeepers in the world during his 17-year career at Goodison Park, fears Everton will be overtaken unless they can find major investment.
Boss David Moyes has so far failed to make any major additions to the squad that finished fifth last term and runners-up in the FA Cup, apart from extending Brazilian striker Jo's loan spell for another year.
And he faces the prospect of a battle to keep England defender Joleon Lescott out of the clutches of Manchester City, with the Toffees expecting an improved bid for the 26-year-old after an initial £15million offer was rejected.
Southall said: "Everton did very well last season, although I was a bit disappointed with the final (performance).
"Now this coming season is going to be a big one. They have to push on.
"But Manchester City are spending tons of money, Spurs look like they will be doing the same and you would expect Aston Villa to keep on spending.
"Now Everton have to find someone to put some money into the club, because if they don't they could find themselves slipping down to eighth or ninth in the table.
"And that is a frightening prospect for a club like Everton. (Chairman) Bill Kenwright has been saying for a long time that the club needs a billionaire, and you do in this day and age."
The former Wales international, speaking in a Sky Sports interview, said: "Now it looks like David Moyes will have to produce a few more miracles on the pitch and hope that the club do find somebody to put a lot of money into Everton.
"It is going to be a really hard job for him. Everton did really well last season and were really consistent, even though they dropped off a bit towards the end of the season.
"Now a bigger squad would help them through and the manager will be able to give players a rest at times.
"I suppose the only good thing is that clubs want to bid for our players now, which hasn't happened for a while."
Lescott is currently with Everton at their training camp in Seattle, ahead of Sunday's friendly with River Plate in Edmonton, Canada.
Manchester City - away in South Africa - will wait until both clubs have returned from their pre-season tours before launching another bid for the player.
Moyes is believed to want closer to £30million for Lescott, money that would be re-invested into the transfer market.
Everton are trying to complete the £6million signing of Swedish international midfielder Rasmus Elms in the next few days.
But there is a clear need for the Merseysiders to spend big to even maintain their current position just outside the top four.
Midfielder Mikel Arteta, who is recovering from a cruciate knee ligament injury, has also shown his concern, saying: "We have to strengthen the team and at the moment we haven't done it.
"Jo is a big name but it is not like a new signing because he was here before with us last season.
"The manager is really good at picking up bargains and he knows how to get 100 per cent out of those players in training and in the games.
"But that does not mean a club like us should not have ambition to fight and try to get the top players.
"If he is able to get the best out of good players, give him a chance to buy big, big names and we will see what we are able to do.
"We are in the Europa League and, when you have that experience, like last season in the UEFA Cup, we need to be ready for that. We cannot wait again until August 31 and the end of the deadline."