The Bombers' interim coach is yet to declare whether he will apply, although his contract as an assistant to former coach Brad Scott runs until the end of 2027 and he intends to stay.
They have lost five games since Solomon took over from Scott, and Essendon were terrible on Sunday, going down to St Kilda by 67 points.
It was the first time under Solomon they had conceded more than 100 points in a game, and Essendon great Matthew Lloyd called it "a hopeless situation".
Lloyd was also asked on Monday if their poor form would hurt Solomon's chances, should he apply. They are a game clear in last place and have won just once this season.
"It's been really tough. (Solomon) is a wonderful person and he just does whatever is right for Essendon," Lloyd said on the AFL website.
"But it's just such a big job, nothing's been able to change, unfortunately for Dean.
"That may be the case, where you state that unfortunately results just take him out of it."
Lloyd was scathing of Essendon under his 2000 premiership teammate, after they were dismantled by the Saints.
The Bombers were well down on disposals and only laid 46 tackles for the game.
"They were beaten up in every area … they are bereft of any belief, confidence, the works," Lloyd said.
"They can't do anything with the footy, and they can't do anything without it.
"In terms of the players, no one goes out there not to try, everyone's trying, but you can just see they are playing with no confidence, there's no belief.
"Even Zach Merrett, he's dominated for years and even he looks a shell of himself.
"It's just a hopeless situation where it's a sad, sad watch."
Asked if his old club are broken, Lloyd replied: "They are, unfortunately".
James Hird, Lloyd's and Solomon's premiership captain, will apply to return as Bombers coach after resigning in 2015.
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