The Holy Blues have moved in to the play-off places under King’s guidance, following the dismissal of Lee Sinnott and John Reed last month.
Though the vacancy hasn’t been formally advertised, the club say they have been impressed by the calibre of applicants.
Chairman, Richard Kane, said: “Morale and performance levels around the club have dramatically improved since the pair were appointed.
“The players have a great deal of respect for Liam and he’s got everything organised and moving in the right direction.
“(Liam and Ross) have both been a part of successful sides and know what it takes to be successful at this level and above. To me it makes perfect sense to extend the interim period, as we continue carefully considering all avenues open to us.”
Gainsborough travel to Basford United in the EVO-STIK League Premier Division this weekend, looking to protect their fifth place.
King added: “There was no hesitation for me and Ross to accept and take the position til the end of the season.
“This works best for everyone in the current situation. As long as performances continue as they are, everyone at the club will be happy.”