The South Africa-based businessman is expected to be among the crowd at Rangers' away match against East Fife today, after a series of meetings.
He was met by a scrum of reporters and photographers after he flew into Glasgow Airport for talks with both side in the Ibrox boardroom power struggle.
As he arrived in Glasgow, Mr King declared the recent disharmony at the club must come to an end.
He arrived shortly after noon, on a flight from Heathrow, and said: "I'm here to see whether I am in a position to facilitate taking the club forward, to get rid of the disunity and lack of harmony both at board level and between the board and the fans.
"I am here for a series of meetings that are at my request. These meetings will remain confidential."
It is understood the tycoon held talks with club shareholders Paul Murray and Jim McColl, as well as current Ibrox powerbrokers James and Sandy Easdale.
Sandy Easdale is one of just two remaining members of the Rangers board, following a recent spate of resignations.
Minutes from the fans' meeting with Mr Murray and Mr McColl revealed the pair were to meet with Mr King, who is tipped to return as chairman. However, they insist "nothing specific has yet been agreed with him".
Earlier this year, Mr King settled a lengthy dispute with the South African Revenue Service after a 10-year battle over contraventions of tax legislation.
Mr King, who invested £20m when Sir David Murray owned Rangers, has said he wants to lead the club's return to football's top tier.
When asked if he could work with the Easdale brothers, Mr King said: "I see no reason not to."
Sandy Easdale said: "I had a very pleasant meeting with Dave King at McGill's Buses in Inchinnan. He's a very interesting man and I enjoyed his company. However our discussion was private and I will be saying nothing further."