If Jiraiya took Naruto to get Sage Mode training, it is likely that he would have taken Minato for the same thing. They were both his supposed child of the prophecy. I believe he attempted the training at least. For Sage Mode you need excellent chakra control, and as far as I can see, Minato's chakra control was superior to Naruto's (at the time Naruto learnt Sage Mode) as he created the Rasengan technique, as well as creating it without a shadow clone. This would take insane chakra control. We just don't know if he has large chakra reserves, but to be able to use his S/T moves and teleport a TBB, I would believe his chakra reserves would be sufficient. There is also the possibility that he has Senju blood but thats another thing altogether XD
Plus he had a contract with the toad.