Taylor injured his Achilles in the Elland Road Championship clash with Brentford on December 17 and has missed United's last three games since.
And while head coach Garry Monk said the 23-year-old's return to training was "imminent", the defender is unlikely to feature in Monday's third round FA Cup clash in Cambridgeshire.
Taylor is now Monk's only injury concern with Eunan O'Kane back in training after his recent groin troubles and with Lewie Coyle also back training after a long lay-off with a knee injury.
Asked for the latest on Taylor ahead of Monday's cup tie, Monk said: "It's a day to day process.
"He's not back in training yet but we are very hopeful that it's very imminent and we need as many players as we can out on the pitch.
"Eunan has come back and Coyley is back in training with us and that's good to have those bodies back into the group.
"I guess Charlie is the only one that is left in the treatment room but it could be imminent. It's just that day to day process."
Assessing whether or not Taylor could make some sort of comeback against Cambridge, Monk reasoned: "Probably not but if he turns up tomorrow in training and ready then who knows?
"We have got a couple of days more (of training) and we will assess the group but at this moment in time it is probably unlikely that he will be involved in the Cambridge game."