After Solomon chose not to put his hand up to be the Bombers' full-time coach, Essendon are closing in announcing a leader as soon as next week.
McVeigh has been tipped to win the job, even ahead of Essendon icon James Hird.
It has led to suggestions of a rift among the trio, something Solomon has strenuously denied.
"We don't know where they've come from - they're rumours," Solomon said on Thursday.
"(McVeigh's been) one of my best mates since the age of 15.
"I've known Hirdy since the age of 17.
"The talks with me potentially not being here next year, whether that stimulated a bit of that conversation, we're unsure.
"But I feel like it's a bit of an episode of (long-running TV soapie) Home and Away.
"There's nothing there. We all want to see this club heading in the right direction."
Solomon, McVeigh and Hird all played together at the Bombers, with the latter two members of Essendon's last premiership in 2000.
The trio also worked together briefly at GWS when McVeigh was the Giants' interim coach in 2022.
Solomon initially declared he would stay on at the Bombers next year, even if he wasn't senior coach.
But his family remains living in northern NSW, complicating matters for him.
"Part of the process of thinking about going in the process for the senior coaching role was sitting down with my family and talking about that," Solomon said.
"My wife and kids live in northern NSW.
"I've had 10 to 11 months away from them at the moment.
"Is that sustainable long-term? It's probably not."
Solomon stressed the next coach didn't need to be an Essendon person, referencing the legendary Kevin Sheedy, who grew up supporting the Bombers but whose playing career was at Richmond.
"He just needs to be the right person," Solomon said.
"A lot of people surrounding our football club are really frustrated.
"We want to be great, and we want to be great really quickly.
"This is a big job and it's an exciting challenge."
12°C