He has just turned 80 and is in poor health.
McLean managed the club between 1971 and 1993, during which time he won three major honours.
This included the club’s only ever Scottish Football League title in 1982/83 and consecutive Scottish League Cup wins in 1979 and 1980.
Remarkably, his team also reached the semi-final of the 1984 European Cup and the UEFA Cup final in 1987.
Broadcaster and United fan Jim Spence said it would be a “fabulous” idea to erect a statue of McLean, who he believes to be one of the greatest managers in Scottish football history.
“I can think of a million reasons to do it but very few reasons not to,” he said.
“He is up there with Jock Stein and Sir Alex Ferguson in what he achieved and I think he absolutely deserves the recognition.
“The success he brought to the club will never ever be matched.”
McLean’s era saw United sweep aside some of the world’s best sides, including AS Monaco, PSV Eindhoven and Werder Bremen.
The team also famously beat Barcelona home and away in 1986/87, to take the Tannadice side’s record against the Catalans to four out of four after two previous victories in 1966/1967.
United have yet to say whether they will officially support the idea, but the club’s chairman, Stephen Thompson, said McLean’s impact is felt all over the city.
He said: “I don’t think you can overstate the impact of Jim McLean not just on Dundee United but the city of Dundee as a whole.
“His Dundee United teams put the city on the map all over Europe and beyond and brought great pride, enjoyment and fantastic occasions to Dundee.”
Mike Barilie, a board member of the The Dundee United Supporters Society, the ArabTRUST, said that things were moving in the right direction.
He said: “There’s not as much pressure on the club to come up with the cash now with various funding options and the rise of crowdfunding.
“The fact that McLean played for Dundee FC should also bring Dee fans on board. He did a lot for the city and really put us on the map.
“We’re pushing for a steering group to be established which will help once we have the club officially on board.
“I just feel that it’s time now. Let’s get on with it.”
Campbell McInally of United Supporter’s club Montecarlo 81, also believes the plan for a statue can be made a reality.
“I think it would a great idea. I’m all for it,” he said.
“There’s no doubt that he was instrumental in setting Dundee United up for some of our greatest successes and put Dundee on the map.
“I always thought that naming the stand after him wasn’t enough. It was a great gesture but just too little in my opinion.”
Lynne Short, a diehard Arab and city development convener, said she also supports the idea.
Ms Short said: “He is an Arab Hero but also played at Dundee and he brought us world famous status. I would definitely be behind that and so should the city.
“I am sure a crowdfunder would get the money together really quickly.”