Elphick joined Hull on loan from Championship rivals Villa in the summer transfer window.
Steve Bruce was the manager of the Villans at the time, but former Brentford boss Dean Smith is now in charge at Villa Park.
The 31-year-old defender joined Villa from Bournemouth in the summer of 2016 for a transfer fee reported by Sky Sports to be worth £3 million and when Roberto Di Matteo was the manager.
Elphick told The Hull Daily Mail: “I’m so appreciative of the gaffer giving me this opportunity to get myself going again.
“I just want to repay him for the platform he’s given me. I promise you, I read things and see things but it hasn’t crossed my mind (about going back to Villa).”
“Perhaps people are putting two and two together and coming to five,” added Elphick. “For me it’s just about the next game and improving what I’ve done so far."
Staying at Hull City
Smith may have plans to bring Elphick back from Hull in the January transfer window, but perhaps the defender is better off at the Tigers.
The former Brighton and Hove Albion star is playing regularly at Hull and seems to be enjoying his football.
Hull are second from bottom in the Championship table at the moment, while Villa are aiming to challenge for playoffs this season.