Welsh, who stood by the call to block Zach Merrett's trade request last year, is adamant the Bombers "won't be pushed around" even as they have sunk further into the doldrums.
Brad Scott was sacked as coach with more than a year remaining on his contract, with former Bombers premiership star Dean Solomon - an ex-teammate of Hird and Welsh - named in the interim role.
There has long been an agitation among powerful groups of Essendon fans for club champion Hird, who was among those to miss out to Scott in 2022, to return to the hot seat.
Hird took the helm in 2010 but was suspended for the 2014 season for bringing the game into disrepute for his role in the Essendon drugs saga.
He then returned to the club but resigned in August 2015 with a final record of 41 wins, 42 losses and one draw.
When asked if he'd spoken to Hird, Welsh said: "I haven't, no.
"We're not ruling anyone in or anyone out of this."
Solomon could also be considered for the full-time gig.
Welsh was pressed on whether he was looking to bring back 'old Essendon'.
"I love the passion of Essendon supporters. I love the history that our supporters talk about, our past players and administrators," Welsh said.
"But by no way means is our decisions around bringing old Essendon people back as an operation to get the Essendon Football Club moving again - that is not in consideration for us at all.
"I hear a lot around 'old Essendon', 'new Essendon', 'boys club'.
"I look at other clubs that, respectfully, Sam Mitchell's gone back to Hawthorn and doing an amazing job, I look at (Justin) Longmuir over in Fremantle, (Josh) Carr's gone back to Port Adelaide.
"So I think there's some really good history around players going back to clubs and the right people for those groups going to those clubs."
Solomon took training on Tuesday morning ahead of Sunday's away game against West Coast.
Essendon join Carlton and incoming Tasmania in the race to land a senior coach.
Welsh wouldn't say whether Essendon would target an experienced mentor like John Longmire or a first-time head coach for the "attractive" job.
Scott, 50, paid the price for Essendon winning just one of their first 11 games, including Friday night's ugly loss to Richmond that anchored the Bombers to the bottom of the ladder.
The board met on Monday and unanimously decided to sack Scott, despite adding a year onto his contract last March, with Welsh informing the coach that night.
Captain Andy McGrath, recovering from a broken jaw, learned of the coaching change on Tuesday morning.
Essendon this year equalled their club-record losing streak of 17 games, which included the final 13 matches of their 2025 campaign.
The Bombers haven't won a final since the 2004 elimination final.
Scott departs after 80 games at the helm, for 29 wins, 50 losses and one draw since his 2022 appointment.
There will also be interest in what this means for contracted Merrett, who is widely expected to again seek a move at season's end.
Essendon last year held Merrett to his contract after the then-skipper demanded a trade to Hawthorn.
When asked if it was a mistake not letting Merrett go in 2025, Welsh said: "No, not at all.
"... We're not going to be pushed around as a club anymore.
"And that was a step and a statement that we are clear in our direction and we're clear with our strategy and what we need to do to push this football club forward again."
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