Speaking at Monday night's best and fairest count, Kernahan said the board would meet in the next few days to discuss what action the club would take following Fevola's drunken antics at the Brownlow Medal count last Monday.
Denying reports the Carlton spearhead had been sacked from the club, Kernahan did not rule out the possibility of Fevola being put on the market during trade week.
"We've seen what happened last week, which no-one is really happy with," he said.
''We all want 'Fev' to be there next year, it's just getting over what happened the other night.''
"Anything is possible –we've got a decision to make."
Speaking after winning his second consecutive John Nicholls Medal as Carlton's best and fairest, Blues captain Chris Judd has thrown his support behind the board, which will meet later in the week to discuss Fevola's situation.
"Essentially it is a board issue – the board will meet with Brendan and speak to him about that," Judd said.
Judd, who said the players had not been involved in any discussions over possible sanctions for Fevola, dismissed suggestions the 2009 Coleman Medallist has played his last game in the navy blue jumper.
"Those sort of rumours fly around at this time of year," he said.
"Speaking to Brendan about it, I guess so much has been said about him in the past week that it is fair he cops a spell now."
The full-forward opted not to attend the Carlton best and fairest count.
