Director Norman Steel told BBC Radio Cumbria Abbott's position would be reviewed as part of an "ongoing" process.
But the club have since moved to deny Steel's comments reflected the feelings of the board.
Jenkins told the club's official website: "As chairman and on behalf of the board of directors I can confirm that there have been no discussions at all about the manager's position and there have been no timeframes set in any way by any member of the board.
"The views expressed to Radio Cumbria on Tuesday night were not representative of the feeling of the board of directors and are not a reflection of our current stance."
The Cumbrians have won just one of their last seven games and are only four points above the relegation zone in npower League One.
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