Leeds United have won just one of their last 11 matches.
The Daily Mirror suggested that Evans was on the brink of the sack, after Leeds were beaten 4-0 by Brighton & Hove Albion on Monday.
Chairman Massimo Cellino has since offered Evans a vote of confidence, but he did similar with Uwe Rosler and David Hockaday just weeks before sacking them.
Evans insists that he is still not concerned about his job security, though, as he works too hard to worry about what might happen in the future.
“I read the words of the Celtic manager [Ronny Deila] this week, when he said ‘how secure is anybody in football these days?’
“I never, ever lay in fear of my job because I work too hard at it and people have to make decisions, whether they want you or they don’t.”
Leeds have won just one of their last 11 matches under Evans’ stewardship, and they have started to slip back down the Championship table.
The Whites have fallen into 18th place, and their performance against Brighton was extremely worrying.
Leeds were 4-0 down before the close of the first half at the AMEX Stadium, as they put in their worst display of the season.
Leeds’ next match comes against Bolton Wanderers, and Evans side will be under pressure to pick up the victory in front of their own supporters.