McVeigh and Bombers president Andrew Welsh will front the media on Tuesday, a day after the appointment was confirmed.
On Sunday night, Hird himself had revealed that McVeigh had won the role. Hird's bid to return to Essendon for a second term as senior coach continues to sharply divide opinion.
Welsh said in the Monday announcement that McVeigh was the "clear standout" candidate, ahead of Hird, Fremantle assistant Jaymie Graham and Adelaide coaching director Murray Davis.
The Bombers are in crisis, finishing bottom this season with the worst win-loss record in club history. There is talk of a pending board challenge and former captain Zach Merrett appears certain to again seek a trade to Hawthorn, a year after his stunning bid was denied by Essendon.
But Lloyd, who played alongside Hird, McVeigh and Welsh at Essendon, predicted the new coach would most likely put the feelers out to his old teammate.
"All I will say is, Mark would love to have James Hird as part of his staff," Lloyd told the Nine Network.
"He (Hird) may say 'you are kidding, there's no way I'm coming, after being overlooked'. But Mark would certainly be open to it."
Hird was an assistant to McVeigh when he was interim GWS senior coach in 2022. McVeigh has been an assistant coach at Sydney since 2023.
Lloyd added that he will not return to the club as part of McVeigh's football department, saying the new coach knows he will be unavailable next year.
He also pleaded with Essendon to support McVeigh properly and spend big on their football staff. Lloyd referred to the unfortunate slogan that the club had for the 2013 season, the year they were punished heavily for their drugs debacle.
The fallout from that saga continues to bedevil Essendon and is a key reason why they are struggling so badly. Hird was suspended as coach for his role in the scandal and then returned, before resigning in 2015.
There has been a growing push for him to come back as coach, but the support in and around the club for Hird is far from unanimous.
"Where is the best development coach out there, in the land? Go after them, because I don't think they have that," Lloyd said.
"There used to be a slogan, 'whatever it takes' - that's where they need to be now.
"They can't afford to have this one go wrong."
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