The 31-year-old is a free agent following his release from Sky Bet Championship club Bolton at the end of last season and he again kept mum last week when quizzed on his next move.
Beckford enjoyed a productive loan spell with Preston, scoring 18 times – seven of which came in the play-offs – as he fired the club into the second tier.
Simon Grayson, his manager at three different clubs, would love to keep him, as would North End supporters, and the fact he has strong bonds in the Deepdale dressing room could be a key factor too.
Tom Clarke and Calum Woods played with him at Huddersfield, Paul Huntington and Neil Kilkenny were his colleagues at Leeds and Chris Humphrey has been part of the same Jamaica squad.
“The list goes on and on of the players that I’ve played with,” said Beckford.
“It’s always nice to have a baseline friendship that you can build upon and experience something like (promotion) with as well. That was amazing.”
Beckford, who said his Wembley hat-trick ranks alongside signing his first professional contract as memories he most cherishes in his career, may also be tempted to reprise his strike partnership with Joe Garner.
The League One player of the year set up two of Beckford’s two goals at Wembley and their alliance was instrumental in the Lilywhites’ excellent form from January onwards.
“It’s brilliant,” Beckford added of his partnership with Garner.
“We’ve got a great understanding of each other’s games – strengths, weaknesses etc etc. It just works really well.”