The Tykes' last-day win at Plymouth saw them escape relegation for the third successive season and Davey's future appeared uncertain following calls from a section of disgruntled fans for him to go.
But Davey said: "I'm manager of the football club and I've not had any sort of feedback to suggest I'm not going to be here after the summer.
"(Owner) Patrick Cryne and I meet every week and we've spoken about the season and discussed the future - about what players we're bringing in and stuff like that and as far as I'm aware nothing's changed."
Newspaper reports have claimed Cryne had given Davey, appointed as Andy Ritchie's successor in November 2006, until Christmas to prove he is the right man to lead Barnsley up the table.
Davey added: "You'd have to ask Patrick about that. I'm manager of this football club and will be busy planning and preparing us for next season. The players have always been behind me and when I was getting stick last season never once did any of them question my ability."