It was revealed by former Newcastle United chairman Freddie Shepherd at the weekend that a clause, which would allow the England striker to move on for £9.5m, expires on Tuesday.
With that deadline looming Allardyce cheekily urged any prospective buyers to make their minds up quickly.
Allardyce: "If that's the case then someone only has until Tuesday!"
Sam Puts Owen Up For Sale!
Owen missed yesterday's win over Juventus with a thigh strain.
Allardyce
"It was an excellent performance and I thought they were terrific. We beat a great team like Juventus and that's what counts.
"It was also important that Newcastle United won with a clean sheet because we hadn't managed that before today and that was the first thing I said to the players.
"I'm delighted for Andy (Carroll) and I thought he took his goal very well. It was unfortunate to lose Luque so early on but I thought Andy did very well when he come on.
"Luque felt his groin, but at least he was sensible about it and decided to come off.
"It's good for the young players to get a bit of experience in the side with so many senior players out.
"We need make sure our injured players are fit as soon as possible because we are running out of time. I wouldn't like to start the season with the side we put out in the second half today."