The 23-year-old played a starring role against Eddie Howe's men when he scored twice in Hereford's 2-1 win over Cherries in September.
Pugh, who is out of contract at Edgar Street this summer, also netted a consolation for the Bulls during their 2-1 defeat at Dean Court in April.
He finished the season as Hereford's leading marksman with 13 goals and the League Two club are desperate to retain his services.
However, despite offering him an improved two-year deal, Pugh has rejected the fresh terms and looks certain to leave.
And sources close to the Daily Echo suggest Cherries are among a host of clubs keen to sign him with Championship new boys Leeds also believed to be tracking him.
Lancastrian Pugh, who started out as an apprentice with Burnley, had spells with Bury and Shrewsbury before moving to Hereford a year ago.
Having been offered a new deal by the Bulls, Pugh would command a compensation fee, which could be determined by a transfer tribunal.
With Cherries boss Howe likely to be in the market for more firepower, Pugh would certainly fit the bill. He can operate on both flanks and has also played as a striker.
Howe has made it clear he will not be commenting on transfer speculation and again politely declined to confirm or deny whether Pugh was among his targets when contacted by the Echo last night.
Meanwhile, Cherries were also remaining tight-lipped over reports claiming they had finalised a deal with Woking for midfielder Harry Arter.
An article which appeared on the Woking official club website yesterday said Arter had agreed a deal with AFC Bournemouth with the fee to be determined by an FA tribunal.
The story appeared just a day after Tooting & Mitcham defender Mitchell Nelson claimed he had signed a three-year deal with Cherries.
However, although both 20-year-olds would again appear to fit Howe's criteria, there has been no official comment or confirmation from Dean Court regarding any new signings since the season came to a close almost a fortnight ago.
Howe unearthed both Anton Robinson and Liam Feeney in the non-league ranks, while he also rescued Mark Molesley by offering the former Grays man a new contract after he had appeared to be heading out of the club following Jimmy Quinn's sacking.
Robinson and Feeney were the last permanent signings made by Howe before Cherries' transfer embargo was tightened in February 2009. And although the ban was loosened in March, any new registrations would still need to be approved by the Football League.