Cantona joined the Red Devils from Leeds United in 1992, a year after Schmeichel moved to Old Trafford from Danish club Brondby. The Frenchman went on to win four titles and two FA Cups, while the former goalkeeper won five league titles, three FA Cups and a Champions League medal during his time at United.
Souness, who achieved success as a player at Anfield, was appointed the Reds manager in 1991. In his three year spell, Liverpool's success in the FA Cup during the 1991/92 season was the only silverware won during the Scot's reign.
He revealed having another Reds legend Bruce Grobbelaar convinced him to not make an approach for Schmeichel, who was a Liverpool fan. Cantona's troubled past was the reason Souness decided against making any approach for the former Marseille man.
"I missed out on two players who went on to become Manchester United legends," Souness wrote in The Sunday Times.
"Ron Yeats, the chief scout then, told me there was a young Danish goalkeeper — Peter Schmeichel — who was a Liverpool fan and willing to pay his own travel and hotel in exchange for some time with us.
"I was trying to ease out Bruce Grobbelaar and that was proving a hassle, plus I had just signed David James, so I thought I could do without a rookie keeper."
On Cantona, Souness said: "Eric Cantona was another I missed out on. We played Auxerre at home and Michel Platini came to see me afterwards."
"He said he had a player for me, a problem boy but a proper player. It was Cantona, but I said the last thing I needed was another problem player. I had 30-pluses I was trying to get out, so I didn't need more hassle. I said I was looking for something else and so it was no thanks."