Midfielder Barry Wilson revealed he had heard of Christie's resignation on Sunday night and expected to learn more details later on Monday.
Inverness have lost each of their three matches so far this term, and Christie, who had been expected to sign a new contract earlier this month, is believed to have walked away from the club.
The latest defeat came at St Mirren on Saturday, as Caley Thistle lost 2-1.
Wilson said: "I think so, I think he's resigned. I heard on Sunday night, I got a tip-off. I think Charlie has just decided that enough's enough.
"We're obviously disappointed that it's come to this."
Christie, 41, is a former player for the Highlands club who took charge at the Tulloch Caledonian Stadium in January 2006.
Wilson said: "We're training later on and maybe Charlie will be there and maybe we'll find out more."