King, the South Africa-based Ibrox chairman, is set to attend the Rangers International Football Club plc annual general meeting on Friday in a rare visit to Glasgow.
But Warburton claims his relationship with the board remains strong through his regular talks with managing director Stewart Robertson and Andrew Dickson, the head of football administration.
Speaking ahead of a board meeting, Warburton said: “We talk to Stewart and Andrew every day. They are the mouthpiece through to the chairman and the board. The lines of communication are always very good.
“There is no sudden announcement, it’s about us constantly talking and putting forward proposals and chatting with Stewart and Andrew. The board meeting is a great chance to sit and talk through, we will present what we think about going forward.”
With third-placed Rangers 11 points behind Ladbrokes Premiership leaders Celtic, King is likely to face questions about his own contribution since he and his allies assumed control in March 2015.
The Glasgow-born businessman, who invested £20million in oldco Rangers before their liquidation, said in May 2014 that he would be willing to invest up to £30million to help the Light Blues compete with Celtic.
King had made £4.5million in loans available to the club before the end of last season with other shareholders taking the total over £10million, and Rangers recently took in a further £2.9million in funding from investors, as revealed in their annual accounts.
Amid the challenge of balancing the books, Warburton feels the club have made major progress on the pitch.
“We have brought in 20-odd players,” said Warburton, who took over in June 2015. “Don’t forget, in 18 months there has been a complete revamp of the squad. You don’t do that without good communication and backing from the board. The club is making progress, which is really important for us.
“I hope very much that the fans see progress being made within the club, on and off the pitch. It’s not just about on the pitch, it’s off the pitch as well. There is only Barrie (McKay), Lee (Wallace) and Kenny (Miller) from the original squad. When we first came in, David (Weir) and I, we had nine players. It’s important to know the size and the scale of the revamp that’s gone on.”
When asked whether he thought fans would accept the time taken to challenge Celtic, Warburton said: “I hope so, I think so. And if you remember the very first press conference we gave 18 months ago, I spoke about communication and the flow of information. It’s their club.
“The more the club does to give them information and let’s them know where we are on and off the pitch, the better it is. It avoids shocks and surprises.
“It’s important to say the club is building. It’s been where it’s been, and it’s important we are moving forward. But we do so at a sensible pace for the club, that’s really important as well.”
The only special resolution at Friday’s meeting, which requires a 75 per cent vote, centres on whether the board can launch a share issue which would allow it to allot shareholdings to new investors. Such a move would bring in money but also dilute the influence of Sports Direct founder Mike Ashley, who remains in legal dispute with the club over commercial and retail contracts.
Warburton said: “All those conversations are above my pay grade. What will be good for me is I find out the end result and we will have a dialogue. But the clever conversations are above my head.”
Meanwhile, Warburton revealed Martyn Waghorn will return to his squad for Saturday’s trip to face Partick Thistle following a rib injury. Midfielder Josh Windass has also shaken off the ankle knock that forced him off against Dundee.