Derby County: Rams 'will be competitive in transfer market'
The Rams are also closing in on a deal for defender Craig Forsyth and are targeting three further signings.
"We have shown ourselves to be able to compete with the players we have been looking at," Rush told BBC Radio Derby.
He also believes their summer dealings will give them a great chance of promotion from the Championship.
Manager Nigel Clough guided Derby to a 10th-place finish this season, only seven points adrift of the play-offs.
"The club has had its best finish for six years," Rush added.
"Nigel and the management team have worked extremely hard. They have built a squad from the bottom up, through the academy and they have a team that is going in the right direction.
"We believe we will have a squad at Derby that will compete at the top of this league. That is our challenge for the next three months and once that business is concluded, it is over to Nigel and the team and away they go.
"We have our targets and are committed to strengthening and having a greatly improved squad by the team the season starts."