It totally depend on the player's versatility attribute as Tharros said.
You can also say that the age is important, as younger players tend to learn faster because of their potential abilities. But as I said before, it depends or their versatiliy, which is an attribute, that unfortunately we're not able to see :/ .
In order to make it faster, it would help a lot if you make the player play in that position, and it's pretty logical, because, how can a player learn to play in a position when he never does in an actual game?
Also it's true what tharros said, if you make a player with high potential ability, and that has not yet reached it's full potential to learn a new position, it's most likely that you're losing time. But if the player has a high versatility, he's young, and has good PA. Then train him in that position, it shouldn't take more than a season for him to get used to that position.
Also, if a player has high versatility it's most likely that the position you're training him for will turn into "Natural" instead of "Accomplished" when he learns it.
I hope it helped