Bryan Smart's six-year-old finished eighth in the Group One Nunthorpe at York last week but is likely to bid for back-to-back victories in the five-furlong Listed event on the Westwood.
Smart's assistant trainer Kevin Edmunds said: "He came out of the Nunthorpe really well and is in good form."
He went on: "He'll probably work on Tuesday and then we'll see how he is, but the Beverley Bullet is likely to be the plan.
"The Nunthorpe was obviously a super race, but the owners were keen to have a go at the big one at York.
"He was brilliant in the Bullet last year and hopefully he might still be progressing.
"He's not quite at the level of Tangerine Trees just yet, but, like his half-brother, he's only going to get better as he gets older.
"The Bullet is a great race and it will obviously mean a lot for his owners, who love having runners at Beverley."
Alpha Delphini is not the only Nunthorpe also-ran in contention as seventh-placed Final Venture and Take Cover, who finished last of 11 runners, are entered too.
Final Venture is one of three possibles for Paul Midgley along with Desert Law and Line Of Reason, while Pipers Note is an eyecatching entry for Ruth Carr following his narrow defeat in the Great St Wilfrid at Ripon.
Kimberella has been given the option by Richard Fahey, while Ornate, Orion's Bow, Judicial and Glenrowan Rose are other notable names among 23 entries.