British Lions lock Jones, who received a yellow card for Wales against England at Twickenham last month, is on course to return for the clash in San Sebastian, Spain following an elbow operation.
Humphreys added: “Alun is making excellent progress at the moment and is ahead of schedule.
“He is one of our best professionals and is leaving no stone unturned. He has given himself a real chance of being fit for Biarritz.
“We have a lot of big rugby to play in the next three weeks and we’re coming to the business end of the season.
“He went into the Wales camp with an injury after the Leicester Tigers game and played through the pain during the Six Nations.
“So maybe the injury was a blessing as he wouldn’t have had a break otherwise.”
