McVeigh was appointed Essendon coach on Monday, with the club opting for the Sydney Swans assistant ahead of fellow former Bombers player Hird.
Hird, who quit as Essendon coach in 2015 after a tenure marred by the club's supplements saga, had pitched for the top job.
"I feel there is significant value James can bring," Welsh told reporters on Tuesday, noting he hopes to speak with Hird later in the day.
"Not just tokenistic, but real value James can bring to our club and playing group."
Hird was an assistant to McVeigh when he was interim GWS senior coach in 2022.
"I love James Hird, he's one of my best mates," McVeigh said.
"It was difficult to go through the process against a good friend.
"I don't fear those people (Hird supporters), I actually embrace how they feel. And I understand it to be fair.
"He's been a constant in my life ... we spoke this morning. It hasn't broken us, we're still together."
McVeigh added he speaks regularly with Hird and will discuss the prospect of a role at Essendon.
"I need to understand where his footy journey is going to go from here," he said.
McVeigh described himself as a "no ego" coach, as he bids to lift the Bombers from the abyss after they collected the wooden spoon in 2026.
"I want to bring the club back to where it needs to be," he said.
