Ride-hailing startup Lyft Inc. hired Qatalyst Partners LP, the boutique investment bank best known for helping tech companies find a buyer, according to people familiar with the matter.

Frank Quattrone, the founder and executive chairman of Qatalyst, has contacted companies including large auto makers about acquiring a stake in Lyft, the people said. It isn’t clear whether Lyft is aiming to sell itself or raise new funding.

Lyft,...