The United manager is set to spend as much as £100m to rebuild the fallen Premier League champions.
Southampton left-back Shaw is one of a host of stars on his wanted list – and former United defender David May insists the 18-year-old would be ideal.
“There is a different player linked to United every day and that is always going to be the case,” he said. “But I think Luke Shaw is a fantastic left-back – the type of player you need. You could have him for the next 10 years easily.
“I think the manager has got to make sure that whoever he brings in is the right type of player.
“You can bring in good players, but you have to play a certain way when you come to United.”
Moyes is planning a summer of unprecedented spending after a miserable first season.
Defeat to Bayern Munich on Wednesday effectively ended United’s campaign and almost certainly means they will miss out on Champions League qualification.
United are seven points adrift of fourth place and face a battle just to secure Europa League football next season.
Moyes insists he is confident they can still attract the game’s top players – but he will face intense competition from Chelsea, Arsenal and City if £20m-rated Shaw becomes available in the summer.
Written by Steve Milne
