After a tumultuous first season on the pitch under new Chinese owners Fosun International, the Midlands side finished the season 15th in the Championship on 58 points - exactly the same haul as the previous season.
Fosun signed 13 players in their first six weeks of ownership last summer, taking the size of Paul Lambert's squad past 30 players, a number that the manager intends to trim to 23 ahead of next season.
"The club is definitely on an upward curve, I think," Edwards, who enjoyed the most prolific season of his career with 10 goals, told the Express & Star. "I think there's a foundation there and that's what we need more than anything.
"We have good owners, a good manager and great fans. Those are the things we need to start off with, but we definitely need additions in the summer.
"We need to bring a bit more quality to the team and trim the squad down as well. There's no way we can have this many players going into next year because it's unhealthy having so many at the training ground. Then it's all about momentum, starting the season well and in the right way and getting this club really rolling forward – it would be a hard thing to stop.
"I know how determined the board are and how desperate the fans are for success. The manager is desperate for it as well. It's key we get more players in the summer and then start the season well. I'm really looking forward to it and hopefully I can be part of it."
Edwards has been with Wolves for more than nine years and surpassed the milestone of 300 appearances for the club earlier this year.