The Terriers looked set to bring in the 28-year-old before the Foxes changed their mind about the deal shortly before the transfer window closed.
"It took a lot of hard work and desire and we almost had it over the line," he told BBC Radio Leeds.
"He wanted to come and we might re-visit it in a few weeks time."
Grayson added: "We're in the hands of the other football club but Jermaine is a player I know well and I like."
Beckford played under Grayson at Leeds United.