The on-loan Leicester man is due to return to the King Power Stadium in the new year but the Terriers chief is hoping to extend his stay in West Yorkshire.
Beckford, 29, joined the club back in September after falling out of favour with Foxes manager Nigel Pearson.
But reported interest from former club Leeds has seen Grayson increase his efforts in hope of holding off his old employers.
"We're working hard to structure a deal with his club," he told the Leicester Mercury.
"There are two willing parties in ourselves and Jermaine and, hopefully, the third are interested too."
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