It was funny actually, I was just asking the same question myself as I've been daring to watch pokemon from the first season again lol. There are a lot of rumours but no sturdy facts as a lot of have mentioned the script writers/story designer did not want Ash to have an active male role model/father figure.
However speculations about Prof Oak or Giovanni have been thrown out, I'm more inclined to Prof. Oak for the fact of his grandson Gary, whose hair style are very alike to that of Ash.
Apparently in the theatre production of Pokemon Live, it was mentioned that Delia, Ash's mother, had previous relations with Giovanni and they once dated, she was going through a rebellious stage, Prof Oak was by her side (they were in a cage apparently) as Giovanni said that times change just like you, or something like that, Delia eventually told Ash, who said he understood, which is probably why, there are rumours linked to Giovanni.