Walsh announced Monday night that the parade would be postponed until Wednesday morning while Boston recovered from its second major winter storm in a week.
He said Tuesday that many people have suggested postponing the parade again — this time until Saturday. He says the players will have scattered by then.
The Patriots beat the Seattle Seahawks 28-24 in Sunday's Super Bowl.
The mayor asked fans attending the parade not to perch on snowbanks because of the dangers involved and to dress appropriately for temperatures expected to be below freezing.