Goalkeeper Murphy has been one of United's players of the season since arriving at Glanford Park in the summer on a free transfer from Sunderland.
The Republic of Ireland international has transformed United's defence, helping turn them into the meanest backline in League One.
Iron fans feared he would be tempted away from North Lincolnshire this summer, but he has declared his intention to stay.
And, as reported by BBC Radio Humberside, midfielder Hinds is also willing to commit his future to the club.