Solomon, who served as a club director last year before stepping down to join the coaching panel, said he had no influence on the board's decision to sack Brad Scott this week.
The 46-year-old has taken the reins as interim coach for the rest of the season, starting with the Bombers' clash with West Coast in Perth on Sunday.
But the full-time role isn't on his agenda.
"I won't even consider that," Solomon said on Thursday.
"While I'm doing this job, I think it's really the wrong thing to do for me to even entertain any thoughts in and around that.
"I've got to knuckle down. My last 48 hours has been chaos and I actually don't have the capacity to take that kind of thought on at the moment.
"So that's where I sit with it and that's where I'll sit with it for the rest of the season."
Solomon denied reports he had a poor working relationship with Scott, speaking of his "respect" for the former coach.
"There's not one part of me that felt there was any bitterness between Brad and I," Solomon said.
He added becoming a senior coach was the "last thing on my mind" when he joined Scott's panel as a back-line coach ahead of the 2026 season.
"Where my heart sits is with this football club," Solomon said.
"It's the reason I got back in my car and drove back down, was at that point in time to support Brad, the players and the staff on the strategy we're on.
"I haven't even considered being senior coach and I won't consider that while I'm in this role."
West Coast premiership coach Adam Simpson and former Port Adelaide coach Ken Hinkley have both stated they believe James Hird is the frontrunner for the vacant Essendon job.
Solomon said he won't be involved in any conversations with the Bombers hierarchy about his 2000 premiership captain, who has already confirmed his interest in returning as coach.
"I love the fact that he feels he's in a position to want to coach again," Solomon said.
"On a personal level I'm glad that's the case. Whether that happens or not, I'm not part of any of those discussions."
Solomon steered clear of declaring what sort of coach he believes Essendon should appoint, but said it did not necessarily need to be someone who has a history with the club.
"There's so many examples both ways ... a lot of success stories," Solomon said.
"You don't have to be an Essendon person to coach this club."
