Representatives of the former England captain, 32, have negotiated terms with Major League Soccer side DC United.
"If the player wants to go - if any player wants to leave - then I'm comfortable with that," said Allardyce.
It is understood Rooney has been offered a contract until the end of the 2020 MLS season. The US transfer window does not open until July.
"My understanding of the situation is there seems to have been some negotiation somewhere along the line," said Allardyce.
"I don't get involved in anything with regards transfers so all I know is there appears to be interest from DC United. Where that lies and where Wayne lies with it I can't tell you at the moment.
"But in terms of clarity of whether Wayne is staying or leaving, I'll find out a little more later when he comes into training."