Biggar limped off during Saturday's 33-28 loss to Australia, giving Gloucester fly-half Hook hope of adding to his 76 international caps.
The 29-year-old will also be considered for the following week's clash with New Zealand, but is not available to face South Africa at the end of the month due to club commitments.
Following the defeat to the Wallabies, Wales have other fitness concerns.
Toulon full-back Leigh Halfpenny will be assessed for concussion, while Rhys Patchell of Cardiff is out with a hamstring injury.
"Next week is going to be a really tough week and we're going to have to back ourselves," said coach Warren Gatland.
"We're going to be a little bit underdone with regards playing time against Fiji but we've got to be good enough with regards the depth of the squad to make a few changes and beat them."