McMullan, who had also been interested in ailing Gretna and Rotherham United, promised substantial backing for the West Lothian club.
On 14 April, he told BBC Sport about his desire to help Livingston win their way back into the Premier League.
Former Powderhall owner Eddie Ramsay failed with an investment bid that would have introduced greyhound racing at Almondvale Stadium.
Owner Pearse Flynn had held talks with an Italian consortium and Livi will continue to search for new investment.
"We are convinced that a joint venture of the type envisaged in this deal still represents the best way to forward," continued the club statement.
"McMullen Properties failed to meet certain criteria set by the board to enable its investment."
Proctor, who coached at Darlington and Hibs, took over from John Robertson in May and led the team to seventh place in a disappointing first season.
Meanwhile, former Livingston chief executive Vivien Kyles has taken up a similar post at Hamilton Park Racecourse.
Kyles left her previous post earlier this week, although she has retained a seat on the board.
She will take over at Hamilton in June from Alastair Warwick, who is heading to Ascot racecourse to become general manager.