So good, in fact, that Manchester United eventually tried to recreate part of Sir Bobby Robson's great Ipswich Town side by signing not only the Dutch midfielder but later striker Alan Brazil.
Reflecting on Ipswich's golden era, Sheepshanks told Football Presse that Mühren's quality often elevated those around him, none more so than Scotland international Brazil.
"Arnold Mühren had the best left foot in football at that time," he said.
"You just knew...
"He made Alan Brazil, who was a phenomenal striker."
Brazil enjoyed the most prolific spell of his career at Portman Road after arriving from Partick Thistle in 1977. Across six seasons he scored 80 goals in 210 appearances, helping Ipswich lift the FA Cup in 1978 and the UEFA Cup in 1981, while also twice finishing runners-up in the old First Division.
For Sheepshanks, however, Brazil's goals cannot be separated from the vision and precision of the man supplying them.
"Manchester United later bought Alan Brazil because they realised that if Arnold Mühren could put the ball in the right place for Alan, there were very few better players who could beat a goalkeeper one-on-one."
It was a partnership that became synonymous with Bobby Robson's outstanding Ipswich side.
Signed from FC Twente in 1978 for around £150,000, Mühren initially arrived amid doubts over whether his technical style would survive the physical demands of English football.
Instead, he became one of the finest overseas players ever to grace the old First Division, forming a superb midfield partnership with fellow Dutchman Frans Thijssen as Ipswich established themselves among Europe's elite.
Mühren himself has always rejected the suggestion that Ipswich's success was built solely around the two Dutchmen.
"We had all international players in our team," he said in a later interview.
"We had English internationals, Scottish internationals and two Dutch internationals. Overall we had a very, very good squad."
Robson's side reached remarkable heights, winning the UEFA Cup in 1981 and challenging Liverpool for domestic honours, while Portman Road became a stage for some of the best football England had to offer.
Manchester United soon came calling.
Following Robson's departure to become England manager in 1982, Ron Atkinson persuaded Mühren to move to Old Trafford, where he immediately helped United lift the FA Cup in his first season, famously converting a penalty in the replay victory over Brighton. He would spend three years at United before returning to Ajax, later adding the European Championship with the Netherlands in 1988 to an already glittering career.
Two years after Mühren's arrival in Manchester, United also signed Brazil from Tottenham Hotspur.
The Scotland striker's spell at Old Trafford never reached the heights of his Ipswich days, with recurring back problems restricting him to 41 appearances in all competitions across two seasons.
Yet Sheepshanks believes United's thinking was understandable.
Few forwards were more clinical when supplied by Mühren.
The Dutchman's ability to measure passes with almost surgical precision allowed Brazil to thrive during the early 1980s, when Ipswich regularly challenged England's biggest clubs despite operating on a fraction of their resources.
Today, Brazil is better known as one of British broadcasting's most recognisable voices after more than two decades presenting TalkSPORT's breakfast show, while Mühren remains revered both at Ipswich and in the Netherlands as one of the country's most elegant midfielders.
Sheepshanks was delighted to hear that Brazil had recently returned to the airwaves after recovering from serious health problems.
"I'm very pleased to tell you he's been terribly ill," he said.
"But he was back on the radio."
For Sheepshanks, it brought back memories of a player who was devastating in front of goal and of a midfielder whose passing could unlock any defence.
Together, Arnold Mühren and Alan Brazil formed one of the most effective partnerships of Ipswich Town's greatest generation – so effective that Manchester United eventually decided they wanted both.