Hitman Borgetti, 32, joined Wanderers in July as Mexico's top scorer with 31 international goals.
But he is yet to start a Premiership game and has slipped to third choice behind Ricardo Vaz Te.
Trotters boss Allardyce said: "He is the saddest player we have. But as a manager you have to be ruthless.
"He's not made the impact Vaz Te has."
Meanwhile, Oman international Ali Al-Habsi has begun training with Bolton ahead of joining the club on January 1 from Norwegian outfit Lyn.