Bukowski, who appeared on Emily Maynard's season of The Bachelorette before joining Bachelor Pad, described The Bachelor as a "great opportunity".
However, he explained that he does not yet feel ready to take on the role.
"I just don't think right now it would be the right time for me to be the Bachelor," he said.
"I think maybe in a year or two I'd be more ready to really take on that role of really putting my heart out there and really committing to a woman and having her be my wife and starting a family with her."
Bukowski added: "I just don't think right now is the right time to be the Bachelor - Bachelor Chris."
A number of names have been linked to the role of The Bachelor, with Bukowski's Bachelorette co-stars Arie Luydendyk Jr and Sean Lowe among the frontrunners.
Olympic swimmer Ryan Lochte has also expressed an interest in appearing in the show, and host Chris Harrison said he would be "great" in the role.