Allardyce has said that there is "no update" on the current situation, but the Everton manager expects a decision to be made either way by the middle of this week.
"There's no update. I said yesterday it's not in my hands now," Allardyce told Sky Sports News. "I've dealt with Wayne, and it's moved on with his representatives and the board from here on in, which I believe may be Wednesday."
Rooney, 33, scored 10 Premier League goals for Everton during the 2017-18 campaign after returning to Goodison Park from Manchester United.
The forward still has 12 months left to run on his contract with the Merseyside outfit.