The 27-year-old claimed that he mistook Steenkamp for an intruder when he fired four gunshots through a toilet door in the early hours of Valentine's Day last year.
Back in March, Price wrote in a magazine column saying that she would not "judge" the double amputee by what various media outlets had reported about the case.
Pistorius began following the former glamour model on Twitter a month later and decided to send her a few private messages.
Price told The Mirror's 3am celebrity section: "He was direct messaging me during the case. It's weird, isn't it? He was saying, 'thanks for the support,' and stuff. Just all general chit-chat. He was the first one to message me.
"Because I mentioned him in my column, he was referencing that. I wasn't exactly supporting him, but everyone who goes through a trial will be the only one who knows what really happened. You're innocent until you're proven guilty."
South African prosecutors have decided to appeal against Pistorius's culpable homicide verdict and five-year sentence.