The pair both played in United's Cup triumph of 1994, beating Rangers 1-0 at Hampden to clinch the trophy for the first time.
United claimed the cup again in 2010, while Tayside rivals St Johnstone, where Cleland is now a coach under manager Tommy Wright, have never been to the final in their 130-year history.
Reminiscing to Sky Sports News about their triumph together ahead of a hugely anticipated clash at Celtic Park, McLaren said: "It was definitely my best day in football.
"It seems a long time ago now and it makes me feel old seeing the pictures of it from 20 years ago but it was fantastic.
"Obviously we were big underdogs that day but we were highly confident and (manager) Ivan Golac had instilled that into us.
"As an ex-United man I've got to back them this Saturday but it's going to be a really tight game."
Jackie McNamara's current United side has a more youthful look these days and McLaren has been thrilled with their progress this season.
"My picks are the young boy up-front Nadir Ciftci, Andrew Robertson at left-back and the wee boy Ryan Gauld - he's a star, isn't he?
"There are youngsters but there are experienced players in there too and a big part of their job will be to calm these youngsters down and make sure everyone's focused on the game."
McLaren also highlighted the danger of St Johnstone's top goalscorer Stevie May but says he would like to think United would win if both sides played their best football.
Cleland, meanwhile, with his eight-year spell at United still in mind, stopped short of picking a winner.
"It's very hard, even though we've beaten them in the last three attempts," he said.
"Both sides know it's going to be a tough game - I don't think anybody can predict this one."