Britain's most famous retiree may be about to swap the dugout for the piano stool in his home city.

After bowing out yesterday from football management, Sir Alex Ferguson has been offered the chance to tinkle the ivories at one of the UK's leading talent schools.

The Glaswegian footballing force of nature, winner of 38 trophies in his 26-year reign, who managed his 1500th and last game as manager of Manchester United yesterday, has said he wants to improve his piano- playing in his retirement.

Having in the past admitted to an enthusiasm for the piano and a fondness for Jerry Lee Lewis, Sir Alex has said he is looking for a piano tutor to help him learn to command the keys as ably as he has footballers in his unparalleled career.

Now the Royal Conservatoire of Scotland in Glasgow, with its £1m fleet of Steinway pianos and some of the leading keyboard staff in the musical education world, is offering lessons as a retirement gift for one of Scotland's most famous sons.

Professor John Wallace, principal of the RCS – whose piano teaching staff include a "premier league" of teachers including Professor Aaron Shorr; piano Professor Fali Pavri; an international fellow in the leading pianist Steven Osborne and an international fellow in Malcolm Martineau – has written to the former manager offering help in one of the musical challenges of his retired life.

Professor Wallace, who is also retiring, wrote to Sir Alex: "Having announced my retirement on the same day as you, I know the necessity of expediting some of those unfulfilled goals in life.

"I would like to invite you to take a course of piano lessons at the best piano department in the world, which happens to be situated on Renfrew Street in your native Glasgow."

Professor Wallace notes in his letter, dated May 13, that a member of his family also aspired to learn the piano when he retired at around the same age. "With fingers that resembled sausages rather than Horowitz-like slender 'ET' appendages, he quickly gave up," he says.

"So you need the best teaching. Which exists in Scotland. We know the score. End of story. Give me a ring ... and we'll fix up the first lesson."

When he announced his retirement, Sir Alex noted his long-held desire to learn to play piano at a competent level.

He said: "My French is not so bad, my piano playing is not very good, so I may have to get a tutor if I have the time."

Sir Alex has said his favourite musicians include "the ballad singers – Frank Sinatra, Nat King Cole and Perry Como".

He once said: "I'd love to sit at a piano alongside Jerry Lee Lewis, because he was the greatest player of all – Chopin, anyone. Jerry Lee was unbelievable, the best I ever heard."

A spokeswoman for the RCS said fees would be the subject of an "arrangement", but the offer of lessons are in the spirit of a retirement gift.

Professor Wallace oversaw the renaming of the former Royal Scottish Academy of Music and Drama as the RCS in 2011.

Before taking up the post he was a distinguished orchestral and solo trumpet player, serving as principal trumpet for two decades.