I don't think they've mentioned his age at all in the story yet. It seems we might find out in the coming chapters tho since Spoiler: spoiler they showed what seemed to be the first One For All user and All For One Just gotta wait and see.
I've not read boku no hero for a loooong time, but I seem to remember that powers began appearing three generations before, or something similar, and he was something like one of the firsts......
Well deku is the 9 owner so atleast he fought 8 others owner of OFA. You can bet that this people reach until 30 years old of their life. All Might itself might reach 40 but by the calculation that previous 8 owner reach at least 30 years old of their life you get 240 years old.
With All Might saying that for him to be living he had to have a power to stop aging, then he must be older than the natural human lifespan. If we assume it to be between 80-100 years old (in modern day), then he should be 100+ years old. There are 9 One for all holders and it's said that deku is from the 4th generation of peoples with quirk. I guess they started counting "quirk generation" after all the society problems with quirks got resolved and humanity got back to modern era (it was said that society got almost destroyed by all that and it took a considerable time to get it in order). For One for all to gain power, it need to be held for a long time, so if we omit exceptions, each holder should have got it for some years at least. All Might seems to have been given it when he was in his younger years, but he could be an exception who had it for a very long time,. Let's say that the average is between 10 to 20 years. That makes a minimum of 80 to 160 years since One for All start existing (1 to 8, not 9, as deku just got it and is the 9th). But it could very well be more or even less, those numbers are only hypoteses. And we can't count AfO as being 0 years old when OfA started, he was most likely already at 40~ years old or something for him to be able to gain so much powers (both quirks and political powers in the shadows). Following all of that, my guess is that he is between 150 and 200 years old at least.
Young All Might with eyes looks weird. He reminds me a bit of lemillion(?). They guy who had the phasing powers.