Allardyce has a hole to fill in his backroom staff after Kevin Keen's recent departure for Liverpool, who parted company with Lee last week.
But he admitted the role he was looking to fill would be lower down the pecking order, not the first-team coach role Lee would be most suited to.
"We are looking to bring in one more coach, but it will not be Sammy," Allardyce said.
"Sammy is a first-team coach, but I have Neil McDonald and Wally Downes here already.
"The only place I need to fill is that of someone to link the Academy and developing players to the first-team squad.
"We are looking at people at the moment and hopefully we will have someone in place in time for the trip to Switzerland at the end of the week."