Interim coach Solomon has opted not to seek the permanent head coach role from next season, leaving four candidates.
Essendon greats James Hird and Mark McVeigh, and club outsiders Jaymie Graham and Murray Davis are going through the final interview process this week.
Solomon, who has just one win from 10 games as caretaker since the sacking of Brad Scott, says the background of the next coach shouldn't necessarily be linked to the Bombers.
"You have just got to be the right person at the right time for the right job," Solomon told reporters on Thursday.
"They're taking their time with the process to be incredibly thorough to ensure they get the right person for this job.
"Whether that is a person who has played for this football club or hasn't played, I think it's irrelevant, I really do."
Hird played 253 games for the Bombers and coached the club from 2011-13 - during the infamous supplements saga - and again for five games in 2015.
McVeigh was a teammate of Hird's during his 232-game career from 1999-2012. He has been an assistant coach at GWS and, currently, at Sydney.
Fremantle assistant Graham and Adelaide's coaching director Davis are the Essendon outsiders vying for the job.
And Solomon said the four were bidding for a role with an exciting future, despite the Bombers' winning only two games this year.
"There's a real development phase we need to go in to," he said.
"Post that, it's going to be quite exciting, but there's a lot of hard work to be done still in the short-term."
Solomon said personally it was "not the right time for me" to apply for the full-time job.
"Like in any decision I make, I go through a process which involves all those things - family, business, where I currently live, the timing of this job, the commitment of this job," he said.
Solomon, who played 158 of his 209 games with Essendon, hoped to remain at the club next year in some capacity.
"It's a little bit unknown over the next couple of weeks until that coach is put in place," he said.
"But we'll work through it and see where it lands."