In one of the sources for Shakespeare's play, Ansaldo, the equivalent figure to Antonio is the godfather of the young man trying to wed the heiress: a generation older. Yet the text, other than possibly implying that Antonio is older (he describes himself as a "tainted weather of the flock", implying, perhaps, tainted with age - and a couple of others are discussed below) doesn't actually give us a definite age for Antonio.
In production, he's frequently played as older than Bassanio, sometimes by as much as ten and fifteen years.
However, Antonio actually describes himself as NOT OLD, in the trial scene:

...it is still [Fortune's] use
To let the wretched man outlive his wealth,
To view with hollow eye and wrinked brow
An age of poverty; from which ling'ring penance
Of such misery doth she cut me off.

Perhaps he just means that he's not poor yet, but it's always seemed to me as if Antonio is saying that he isn't old yet (it is, actually, a thought that appears elsewhere in Shakespeare: in Julius Caesar, the conspirators try to argue that 'he that cuts off twenty years of life cuts off so many years of fearing death', rather imporbably). That could make him, say mid-40s to Bassanio's 25-35?
And he does seem set apart from the rest of the young men - age would be one way to do it.
But, unfortunately, there's no final answer in the text for this one. Sorry! Hope it helps anyway!