Wanderers secured four consecutive top-half finishes under Sam Allardyce between 2003-04 and 2006-07, but have spent most of their time around the lower reaches of the table since.
Owen Coyle guided the team out of the relegation zone and to the safety of 14th in the last campaign after taking over from Gary Megson in January, and Davies feels Bolton can continue on the up in the coming season.
Asked about the potential for a push for Europe, Davies said: "It would be great if we could challenge for that position come March or April time - if we can be in and around the top 10.
"If we can challenge for a top-10 finish it would be a stepping stone for us because the last two or three seasons have been all about staying up.
"When you are playing in those conditions year in, year out it's difficult to take mentally and you have to be really strong.
"You have to have a good spirit, which we have got and that has kept us up really.
"But I think we have got everything in place now - we have got a good squad, we have got the manager and the backroom staff.
"Hopefully the fans will come back to the Reebok and get behind us, and if we get off to a good start, who knows?"
Club captain Davies has experienced plenty of good times with Bolton during his seven seasons at the Reebok Stadium, but the 33-year-old is still yet to win the win the England call-up he has frequently been tipped for over the years.
The Sheffield-born striker, who has revealed he was approached at the end of 2009-10 about playing for Scotland, accepts he is now unlikely to get the chance to wear the Three Lions jersey - but has not given up on it entirely.
"I don't know too much about my family background but I don't think there are any Scottish relatives in there, so as far as I'm concerned, I'm English," Davies said.
"You never say never, but I don't think it (playing for England) is going to happen now, at my age.
"If you get off to a good start and bang in a few goals you never know.
"It's not something I'm going to rule out altogether."
Wanderers conclude their pre-season preparations by hosting Osasuna tonight before getting their Premier League campaign under way at home against Fulham on August 14.