The Lyft app is demonstrated on an Apple iPhone 5s.

Lyft this week set out to raise a new round of funding to help it catch up to the massive war chest raised by its rival Uber, sources said.

The ride-hailing company company—which was last valued at $850 million—is in the midst of its efforts, with what one person close to the situation said was a "significantly" higher valuation. Both that and the amount to be raised are still in flux.