An early preferred candidate of Bombers president Andrew Welsh, Solomon's hopes of winning the job are dwindling after six straight defeats - the latest a 90-point mauling by Brisbane last Sunday.
Hird has declared he is "all in" on Essendon and has met with the club to talk about a coaching comeback, 11 years after he quit during the supplements saga.
If Solomon doesn't stay on as senior coach, the 2000 Essendon premiership player has already stated he will stay involved at the club next year.
It is realistic Solomon could still work as an assistant under his former captain if Hird won the job.
"I haven't spoken to Hirdy for a couple of weeks now," Solomon said on Wednesday.
"He's expressed his interest in the job and he's part of the process, but outside of that I haven't spoken to Hirdy."
Solomon expects to get a "tap on the shoulder" from Welsh and Bombers chief executive Tim Roberts about his plans beyond this season.
But Solomon isn't willing to say if he will formally go through the process to become the permanent coach.
"I just haven't had time to think about it," Solomon said.
"This role is full-on, and especially the current-day situation we're in.
"I spend 23 hours a day trying to work out how we can get this club back to being really competitive in the short term.
"I know that might be hard to believe, but that's honestly where my head is at, and literally it consumes all of you in this role."
Essendon have won just once in their past 30 matches amid one of the lowest points in the former powerhouse club's history.
The Bombers are set to collect their first wooden spoon since 2016 - the year the club was forced to use top-up players because of the supplements saga.
In a reset for the club, Essendon held a light training session back at their spiritual home at Windy Hill on Wednesday.
Players were joined by the club's AFLW team, who continue to play some of their matches at the historic venue, instead of the current headquarters at Tullamarine.
It comes days after young forward Nate Caddy signed a contract extension until the end of 2031 in a huge show of faith in the battling club.
"We know we're wading through a swamp, and it's hard, but there's only one way out of this, and he wants to be part of the solution," Solomon said of Caddy.
"This club will turn. There is no sugar hit. There's no short-term fix. There's no magic wand.
"It's just going to take the right decisions and getting the right people in the right places and rolling our sleeves up together ... he wants to be part of that."
Solomon threw his support behind key defender-turned-forward Ben McKay, who recorded just two possessions in the club's VFL game on Sunday.
"The last conversation I had with him late last week was about for him to have a think ... what he prefers forward or back," Solomon said.
"Initially (the move forward) freed him up, he had 13 shots in four games at AFL level.
"We felt like he can improve his game without the ball in his hand, and he's gone to the VFL to work on that.
"He'll keep working and he'll be fine."
Essendon face resurgent GWS, hunting a finals spot, in a daunting assignment at Marvel Stadium on Sunday.
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