The Preston boss wants to keep the ex-Leeds striker, especially if his side earns promotion to the Championship.
The former Leeds United forward has recently been released by Bolton Wanderers ahead of the summer and is currently finishing a loan spell at Preston.
And Grayson would like to ensure Beckford stays at Deepdale, something that will be made easier if Preston earn promotion to the Championship, he says.
The ex-Leeds coach told reporters: "We've obviously put lists together for plan A and plan B. But the one thing you'll say about Jermaine is he loves being here. He's played a big part in the success but he's also enjoying working with me and Glynn [Snodin].
"We like to think we've got the best out of him, he's a happy lad, so let's hope we can make a decision easier by getting into the Championship."
The news would normally be seen as a passing interest for Leeds fans - a former player could be extending his stay at the club he is on loan at.
But there are two interesting factors at play here. Firstly, Beckford may end up returning to Elland Road once again should he stay at Preston if they achieve promotion (although he already has playing for other sides).
Secondly, though, some Leeds fans have recently expressed their views on Twitter that they would love to see the 31-year-old back at the Yorkshire club. The Whites have been extremely short of goals lately, of course, and here is a free agent that is popular with supporters. But the former Leeds striker could be staying with the former Leeds manager instead.