Konsa is expected to leave The Valley during the January transfer window with Jurgen Klopp's men reportedly leading the chase after hijacking the Toffees' bid to sign the £4m-rated ($5.6m) England youth international, who has made 30 appearances in all competitions this season.
Liverpool and Everton have pried two of Charlton's most promising youth graduates away from The Valley in recent seasons - Liverpool signed Joe Gomez in the summer of 2015 while Everton pilfered Ademola Lookman from the Addicks last year.
Murray, who was keen to lavish praise on Konsa, thinks both the player and his agent have eyes on a move to the Premier League and the riches it inevitably brings.
"Ezri has been a wonderful player for us," Murray told the Charlton Supporters' Trust, relayed by the News Shopper. "He's played well week in, week out even though he must be aware that a number of Premier League clubs are looking at him.
"He's put in consistently good performances, so I've got nothing but praise for him. However, he and his agent would love to get a deal like Joe Gomez and Ademola Lookman because playing in the Premier League, earning lots of money is appealing. I think one has to be realistic on that."
Charlton owner Roland Duchatelet may be keen to cash in on Konsa - the unpopular Belgian has already sold Ricky Holmes to Wigan Athletic this month - but Murray, who joined the Addicks board in the 1990s, does not think the former Standard Liege chief will jump at the chance to sell to Everton or Liverpool because it may lower the price of the club he is trying to offload.
"There are a number of dynamics on the Konsa deal - he would be a very substantial asset and I feel any person that is potentially looking to buy the club would see him as one of our potential playing assets," he said.
"The assumption would be if he goes the price may come down. Therefore I believe the incentive for Roland to sell him is not quite as forceful.
"I'm not trying to undermine any negotiations, I'm just talking about logic. We have not had a firm offer but the trouble with the transfer window is you never know."