The Whites chose to part company with Marsch amid a run of poor results, but have found it tough to tempt a successor to take charge so far.
Feyenoord boss Arne Slot has rebuffed overtures from Leeds, while West Brom manager Carlos Corberan penned a new contract at the Hawthorns.
Rayo Vallecano coach Andoni Iraola is of interest to Leeds, but the Spanish side are firmly set against losing him.
Nevertheless, Kinnear is confident Leeds are on course to make an appointment, even if he admits doing so in mid-season is a challenge.
He wrote in Leeds’ official matchday programme: “The search for a new head coach is well advanced.
“The task is being able to align our list of prospects – which has been built and evolved over many seasons – with current availability and the openness of candidates to accept a new role in mid-season.
“While we have confidence in the caretaker team, we know the importance of a prompt appointment and, if Victor [Orta] and I are in any doubt, we have Andrea’s [Radrizzani] Twitter account to keep the pressure on!”
Leeds are due to play host to Manchester United at Elland Road this afternoon and will aim for three points after holding the Red Devils to a draw in midweek.
