United manager Simon Grayson told his club website: "Enoch needs to play regular football and hopefully this will enable him to do so.
"He was very unfortunate last season, but opportunities have been limited for him this season."
Showunmi made his senior breakthrough with Luton Town before spending two years with Bristol City during which he had a loan spell with Sheffield Wednesday.
He joined League One outfit Leeds in 2008 and made only 28 appearances, scoring six goals, hitting the net for the last time in his final start in a Carling Cup victory over Darlington in August.
However, he has been prolific scorer for the club's reserves.
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