Roman Romanov backed the caretaker at the club's AGM on Friday and pleaded with fans to "give Frail a chance."
Hearts have improved since Frail was promoted to caretaker in January. Having narrowly missed out on a top six finish, Frail believes he can do better next year.
He said: "I would like to think that I have learned enough to do the job. People are always saying they want more experience but sometimes the only way to get the experience is to throw someone in.
"I am not silly enough to think that I would be a fans' favourite if I was given the job but when you look at the results that we have all achieved since January then we could have been sitting third in the league.
"From where we have come from - and the quality that we have lost - then I would look upon that as a real positive.
"If we can get more, or better, quality in over the next year then who knows what we can do.
"But, again, I am leaving the decisions up to the owner over who he wants to bring in. We'll wait and see what happens."
