Ivory Coast-born Djetou is a free agent after a spell in Italy and the former Fulham star is a perfect fit for Wanderers.
However, Djetou took up an offer from German side Duisburg to train for a few days and is yet to commit to a trip to the Reebok.
Allardyce is without full-back Nicky Hunt for more than a month and could be stretched with Bolton in the UEFA Cup group stages.
With the transfer window closed until January 1, Wanderers' only hope of easing the strain is to find unemployed or out of contract players.
"We know he's available, but we haven't got much further in discovering whether he wants to come to England or not," Allardyce said.
"We are scouring the world for out of work players, but the problem is that, if they are out of work, they haven't been competing at any sort of level. And if you find one, you're talking six to eight weeks before you get him to the level you want him to be at."
Meanwhile, Jay Jay Okocha could be out for 4 weeks after pulling his groin in the 2-1 defeat to Wigan on Sunday.