Three women have been attacked by an alleged serial sex offender in the space of two hours in Melbourne's inner-east, including one victim who was assaulted as she tried to open her front door.

Police are hunting the man they believe waited in laneways before ambushing his victims, attacking all three women in Richmond and Abbotsford in the early hours of last Sunday morning.

Police want to speak to this man in relation to three sexual assaults in Melbourne's inner-east. Credit:Victoria Police

Officers fear there may be more victims who are yet to come forward and hope the alleged attacker's distinctive walk and clothing will help identify him.

"Trends in the attacks show that he would approach the victim from behind and would grab them. There is some connection of him hanging around laneways showing predatory behaviour waiting for his victim to appear," Detective Inspector Stephen Wilson said.