The pair have been informed their services are no longer required following the exit of Sir Alex Ferguson. And that may not be the end of the cull with Moyes still to inform coach Rene Meulensteen whether he will be retained.
Formerly a United player under Ferguson, Phelan has been back at Old Trafford since 1999, taking up a position on the first-team coaching staff two years later and replacing Carlos Queiroz as assistant in 2008.
Steele, who has been credited with the development of David de Gea over the past two years, replaced Tony Coton in 2008.
"I would like to put on record the club's thanks for everything Mike and Eric have done," said Moyes. "I will be looking to appoint my own members of coaching staff at some point in the future. However, I'd like to take this opportunity to give them both our best wishes for their future careers."
Executive vice-chairman Ed Woodward added: "I'd like to thank Eric and Mick for the enormous contributions they have made to the success of Manchester United in their time here.
"Their professionalism, ability and diligence have been a credit. They are top-class football men and everyone here wishes them well for long and successful careers."
Moyes is yet to decide who will replace Phelan and Steele, who both have extensive trophy-winning experience.
However, as the former Everton boss likes to involve himself in training sessions, it is hardly a surprise at least one senior member of United's coaching staff should find themselves surplus to requirements.
Former Leeds midfielder Jimmy Lumsden is a long-time confidante, whilst Moyes has worked with ex-England keeper Chris Woods at Everton. In addition, Phil Neville has just left Goodison Park and is yet to decide whether to pursue a coaching career.
Source: PA
Source: PA