Food-delivery startup DoorDash Inc. is arming itself with new funding as two of its rivals prepare for initial public offerings.

The venture-backed company is in the process of raising roughly $500 million at a valuation of more than $6 billion, and that might approach $7 billion, according to a person familiar with the situation. That valuation range would be four to five times where DoorDash was valued in a financing round less than a year ago.