Baptiste is available on a free transfer when his contract at Blackpool expires next month.
Derby were interested in the 27-year-old before being put off by what Rush described as "eye-watering" salary requests, and Baptiste looks set to join Bolton instead.
"He is someone that we asked about," Rush told the Derby Telegraph.
"I spoke to his agent and with the best will in the world, the money he was asking for was eye-watering. I don't think many clubs in our division could afford him.
"There is a difference between ambition and bad management. I don't think Derby fans would have thanked me for bringing him in on that kind of money."