The Churchill Downs star failed a post-race test as his sample had been found to contain 21 picograms of the anti-inflammatory medication betamethasone.
Baffert insists he is innocent of any wrongdoing and stated at the weekend Medina Spirit had not been given betamethasone to his knowledge, calling the failed test a "gut punch".
On Tuesday, Baffert issued a statement via his lawyer Craig Robertson in which he revealed an anti-fungal ointment prescribed for a case of dermatitis could potentially be to blame, as his own investigations continue.
He said: "Following the Santa Anita Derby, Medina Spirit developed dermatitis on his hind end. I had him checked out by my veterinarian who recommended the use of an anti-fungal ointment called Otomax.
"The veterinary recommendation was to apply this ointment daily to give the horse relief, help heal the dermatitis and prevent it from spreading. My barn followed this recommendation and Medina Spirit was treated with Otomax once a day up until the day before the Kentucky Derby.
"Yesterday, I was informed that one of the substances in Otomax is betamethasone. While we do not know definitively that this was the source of the alleged 21 picograms found in Medina Spirit's post-race blood sample, and our investigation is continuing, I have been told by equine pharmacology experts that this could explain the test results. As such, I wanted to be forthright about this fact as soon as I learned of this information.
"As I have stated, my investigation is continuing and we do not know for sure if this ointment was the cause of the test results or if the test results are even accurate, as they have yet to be confirmed by the split sample.
"However, again, I have been told that a finding of a small amount, such as 21 picograms, could be consistent with application of this type of ointment."
Baffert added: "In the meantime, I want to reiterate two points I made when this matter initially came to light.
"First, I had no knowledge of how betamethasone could have possibly found its way into Medina Spirit (until now), and this has never been a case of attempting to game the system or get an unfair advantage.
"Second, horse racing must address its regulatory problem when it comes to substances which can innocuously find their way into a horse's system at the picogram (which is a trillionth of a gram) level. Medina Spirit earned his Kentucky Derby win, and my pharmacologists have told me that 21 picograms of betamethasone would have had no effect on the outcome of the race.
"Medina Spirit is a deserved champion and I will continue to fight for him."
Baffert plans to run Medina Spirit in the second leg of the Triple Crown, Saturday's Preakness Stakes at Pimlico, with the colt having arrived at the track on Monday.