The Wales international ended up moving to Real Madrid for a world record fee, but the Scottish boss admitted he would have loved to have had the flying winger at his disposal at Old Trafford.
"When I got the job, I thought Gareth Bale would have been a super Manchester United player,” Moyes is quoted as saying by Marca.
"I thought he had that look about him that you expect to see in Manchester United players.
"He was someone we were really interested in but he had his heart set on Real Madrid."
Moyes has since moved on to manager Real Sociedad, with the former Everton chief improving the Basque club’s fortunes in La Liga.
The Anoeta club are set to face Real Madrid today, with Carlo Ancelotti’s men leading the division and the current European champions.
Moyes has stated that he remembers his match-ups with the Italian during his time in the Chelsea dugout and holds his opposite number in high regard.
“Carlo Ancelotti is one of the best managers in the world,” he continued.
"His success in the Champions League last year was fantastic and he is a coach with a wealth of experience. We've crossed paths on occasion when I managed Everton and he was at Chelsea.”
Moyes has led Sociedad to 11th in the league table and recorded a shock 1-0 victory over Barcelona at the start of the year.
However, his side are massive underdogs in travelling to the Santiago Bernabeu today, even though the hosts are without the suspended Cristiano Ronaldo.