Allardyce repeated an earlier claim that the former England international's potential move to Major League Soccer side DC United was "not in my hands now".
However, it looks like there will be an update this week, with Allardyce adding on Sky Sports' Season Review - Managers Special: "It's moved on with his representative and the board from here, which I believe may be Wednesday."
Rooney finished the season as the Toffees' leading scorer with 11 goals, but was absent for Everton's last game of the season with a knee injury.
Of his own future, Allardyce added: "Who knows what's going to happen next?
"The season has finished, I'm going to have a meeting with (owner) Farhad (Moshiri) this week and then I'm going on my holidays."