In his first press conference after Brad Scott was sacked as Bombers coach last month, Solomon declared he would not be seeking the position on a full-time basis.
But a bombshell report this week stated Solomon is Welsh's preferred candidate for the top job, even over James Hird.
But Solomon, who played in Essendon's last premiership back in 2000, is adamant coaching the club beyond this year is not on his radar and is yet to speak with Welsh.
"The club is obviously working behind the scenes about what the next coach would look like, time frames," Solomon said after Essendon's 45-point defeat to Melbourne on Saturday.
"I have no knowledge and I didn't want to know any of that, I still don't want to know any of that, because I've got to focus on what I've got to focus on.
"The most important role I need to play right now is ensuring we have momentum into the finish line here, because if we fall away, it can do a fair bit of damage.
"My sole focus is on these players and the staff, ensuring they're in a good headspace, and we're playing the right way, and we hit this finish line with momentum."
The Bombers have lost all three games since Solomon took charge, slumping to 1-13 and heading towards the club's first wooden spoon since 2016.
Hird, who infamously coached Essendon during the supplements saga, has declared he would like to lead the Bombers again in what would one of football's most remarkable comebacks.
Solomon, Hird and Welsh are former teammates at the Bombers.
Essendon trailed the Demons by 41 points at halftime, but almost broke even after that.
Solomon denied the ongoing intrigue surrounding Essendon and the coaching position had any impact on the players.
"It's not why they're flat, and I'm unsure how much they (the players) read or take on," he said.
"I know there's going to be a lot of noise around, but I'm right in the middle here, focusing what I need to focus.
"I haven't heard or had any conversations about any of that, about who's our next coach, so I'm pretty confident they're (players) not thinking about that, and that is absolutely not the reason that we had the half we had at the start."
Essendon were badly beaten in the midfield, forcing former captain Zach Merrett to shift back into the centre square.
With Merrett expected to depart the club at season's end, following his failed trade attempt to Hawthorn last year, the Bombers have moved him to halfback.
A potentially season-ending shoulder injury to young gun Archie Roberts, who has been a shining light in defence, could also help keep him in the backline.
"I'd like to continue with him at halfback," Solomon said of Merrett.
"Obviously got other coaches to discuss that with, but it'll depend on team balance, too.
"I'd love to settle him at halfback, so we can continue to drive the ball forward a lot more than what we currently are."
Essendon are hoping a quad concern that forced swingman Kyle Langford from the field against the Demons is minor.
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