Moyes traded the hot-seat at Goodison Park for that at Old Trafford at the start of the summer, bringing to an end an 11-year stay on Merseyside.
Throughout much of that tenure, he admits to having been an admirer of Germany international Kiessling.
The 29-year-old has been a regular source of goals throughout a seven-year stint at Bayer Leverkusen, allowing him to attract admiring glances from afar on a regular basis.
Kiessling has often been linked with a move to England, but Moyes concedes he was never in a position at Everton to put the necessary financial package in place.
Moyes, who will line his United side up against Kiessling and Leverkusen in their opening UEFA Champions League fixture of the new season on Tuesday, told Sport Bild: "In all the years I was at Everton, I followed him all the time.
"But the money was sadly lacking.
"I have great respect for him. He is a great player who is strong with his head and his feet."