The field of Republican presidential candidates keeps getting narrower, but George Allen still hasn’t picked a horse. At least, not outside of the voting booth.

Allen — the former Virginia governor and senator running to succeed retiring Sen. James Webb (D) — has stayed neutral throughout the White House contest, even as more and more GOP luminaries have coalesced around former Massachusetts governor Mitt Romney.

Does Mitt Romney have George Allen’s support? It’s not clear. (Evan Vucci/Associated Press)

Allen did add that he would “undoubtedly support our nominee,” and it’s possible he’s already helped Romney in private. Allen voted in Virginia’s March 6 Republican primary, when only Romney and Rep. Ron Paul (Texas) were on the ballot, though he hasn’t said which man got his nod.

Allen faces some primary competition of his own on June 12, though he is considered the prohibitive favorite. Of the three candidates challenging him for the Republican nomination, at least two — former Virginia Tea Party Patriots head Jamie Radtke and Del. Bob Marshall (Prince William) — are running to Allen’s right, and it’s not clear whether endorsing Romney would help him in that contest.

Virginia Gov. Robert McDonnell and Lt. Gov. Bill Bolling have both endorsed and campaigned for Romney (Bolling is his Virginia campaign chairman), while Attorney General Ken Cuccinelli has said he doesn’t plan to back a candidate.