Literary critics cannot agree on the identity of the old man, but there are several possibilities of who this mysterious character may be. First, it's possible that he is Death itself. When the old man creates the comparison of Death as a mother, it suggests that death should not be viewed as a frightening thought - instead, death provides comfort and respite from suffering.  He also seems to know more than he should: he says to the men, "When you are old -- if you should live til then." He foreshadows the upcoming deaths of the young men. 

Another possibility is that the man is an angel of death, a sort of precursor to an upcoming demise. This would also explain the comforting view of death and how the character seems to know future events. 

A final, more literal possibility is that the man simple is just an old man who is wise and sees the men for what they are -- selfish. The identity really isn't important: what matters is that this man is the catalyst for the men finding the gold under the tree, which leads to their deaths through their own selfishness and greed. 

The old man figure in the Pardoner’s Tale (in Geoffrey Chaucer’s The Canterbury Tales) is a rich, complex and mystical character that can be given multiple interpretations. The old man can be “death” itself or a representation of death as he sends the three young men, who are looking for death, to an Oak tree where they find treasure and, ultimately, die. In other words, he sends them to a place where they find death or death finds them.

One of the “rioters” calls him the death’s spy. But since this comes from a drunken, stupid man, the readers can doubt its validity. 

Hear my true word, since you are his own spy,

Tell where he is or you shall rue it, aye.

The young men find the old man very disgusting and as someone who should have died by now. The old man says that he wants to die but he cannot, as even death doesn’t want him.

Not even Death, alas! my life will take;

What, then, could the old man symbolize? He could be an allegorical representation of something that cannot die or end. Death? Human sins? Experience? He calls himself a restless soul who must continue wandering until Mother Earth lets him in. Whatever he is, he is definitely not an angel or hermit figure. He is clever as he confuses and tricks the young men who are impatiently looking for death. They all die because he sends them there. Like the Pardoner, the old man is a hypocrite who blesses the young men and replies patiently to their abuses, but deceives them by sending them to a crooked path where death claims them.

See you that oak? Right there you shall him find.

God save you, Who redeemed all humankind.

It is quite possible that the old man is death itself. Although the old man complains a little about being so old and wishing that death would find him, it isn't proof that he is just an old man. He takes advantage of the drunken youngsters' eagerness to find death by pointing them in death's direction. Although the young men didn't quite find what they thought they were looking for, they certainly did find death. In that manner, the old man could very well be the Grim Reaper himself gathering a new group of victims.