The municipality shall first notify each private owner interested of the plan proposed and of the level up to which such lots are to be filled and of the general plan proposed and such private owners may, if they see fit, arrange to fill up their lands at their own expense, such filling up to be done either prior to or contemporaneously with the filling done by the city, and to be in accord with the general plan adopted. And the owner of any such land shall be entitled to use the mud or soil in the bed of the river in front of such land for the purpose of filling up his land, in preference to any other, to the extent necessary to fill such lands.