"We have got a lot of riches in that area," defence coach Shaun Edwards told a news conference on Tuesday. "We have a big decision to make there."
It will be a choice for coach Warren Gatland of either Anscombe or Biggar as Patchell will not be considered for this weekend's test.
Patchell has not played since suffering concussion at the start of last month playing for the Scarlets against the Ospreys but although now passed fit is deemed not match ready.
But England-based Biggar joined up with the squad on Monday after being unable to play in Saturday's 21-10 win over Scotland because the test fell outside of the international window, and he will be pushing to resume his role as first choice pivot.
But New Zealand-born Anscombe had a steady game and will also be hoping for the nod again from Gatland when the team is named on Thursday.
"It's great to have competition, I know it is the glamour position, as a pivot you control the game. We will weigh it up over the next couple of days," Edwards said.
Wales have also confirmed hooker Ken Owens and flanker Ellis Jenkins are fit, but tight-head prop Samson Lee, who is battling a hamstring problem, is out for Saturday's test at the Principality Stadium.
"Samson is a very strong scrummager, but we have Tomas Francis and we are strong in that tight-head position at the moment," said Edwards.
Owens suffered a broken nose during the victory over Scotland while Jenkins, who was not involved, has recovered from a shoulder injury.
(Reporting by Mark Gleeson; Editing by Hugh Lawson)
