The new pool would replace the 25m one at the Moorways Sports Centre. Plans include closing Moorways' running track and possibly selling-off the land.
Money raised would help improve the university's running tack and building a big stadium for spectators.
The council said the idea was still in very early planning stages.
No time frame has been set.
A feasibility study is to be undertaken and if the plans are well received, a public consultation will held at the start of next year.
Council leader Chris Williamson said: "All in all it will significantly advance sporting facilities in Derby and that's got to be good.
"To provide an Olympic-sized swimming pool in a city of Derby's size is a tremendous step forward and coming as we hope it will do - ahead of the Olympic games.
"If we can provide this level of training facility in Derby who knows, maybe we may be able to train a future Olympic champion coming from Derby."
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