"I would hope to have a new manager in place before our next game with Queen's Park Rangers a week on Saturday," he said. "If we don't, I might have to get my own tracksuit out! But, seriously, negotiations are progressing."
Whoever takes charge will have to get City back into the Premiership or risk losing Georgiou Kinkladze.
Lee has always insisted that Kinkladze is not for sale, but he recognises that the midfielder might not wish to play another season in the First Division.
"Gio was at my house this week and he was quite happy," Lee said. "But perhaps he would not show for playing another season in this league."
Lee realises that his own future at City is being put in jeopardy by his willingness to talk to potential investors. "If people get total control of the club, they can pick their own chairman," Lee, who owns 29.9 per cent of the shares in City, said. "In any event, if the board here don't fancy me as chairman, they can get rid of me."
Mark Guterman, the chairman of Third Division Chester, was expected to plough pounds 35m into Maine Road in an effort to secure the future of Chester as a feeder club for the Manchester side. The announcement, however, was postponed because of "the delicate nature of the negotiations".
Lee remains optimistic and is looking forward to the challenge of the next few weeks. "We need to get things sorted out - and that includes the managerial front. That is part of the plan as well and we are hoping to get that sorted out before the next match."