Biggar was unavailable for Wales' Six Nations clash with Italy in Cardiff last Saturday following a grade-one hamstring strain.
But the inspirational fly-half is hopeful he will be fully fit for the Welsh region's derby clash with the Dragons in two days time.
"It's been a frustrating campaign and the injury has topped it all off," said Biggar, who missed out to Scarlets star Stephen Jones in all five of this season's Six Nations games despite making an impression at the highest level during the autumn internationals.
"I had a hamstring tweak in the Magners League game at Edinburgh last month and failed to recover to play in the rest of the Six Nations.
"It's frustrating because I believe I would have had the chance to face Italy.
"But I hope to be fit and raring to go to face the Dragons and then the big one against Biarritz."
The Ospreys travel to Rodney Parade to meet a Dragons side just a place behind them in the Magners League standings.
They then host the Scarlets on April 2 before travelling to Ravenhill to meet Ulster in a rearranged fixture on April 13.
Having topped the table earlier this month, the Ospreys are currently just outside the Play-Off zone with six games left to play.
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