The drain of players to France is a major concern for the Welsh Rugby Union and the regions.
Jamie Roberts has confirmed he is leaving the Cardiff Blues at the end of the season and is expected to join Wales team-mates Gethin Jenkins, Mike Phillips, James Hook and Luke Charteris in France next summer.
But Biggar has not opted to join them on the other side of channel, preferring to continue to ply his trade domestically.
"I'm hoping to sort things out with the Ospreys sooner rather than later," he said.
"That's my aim. I want to be staying here and I want to be playing week-in, week-out.
"The bottom line is I want to get things sorted as quickly as possible, and hopefully we can do that."
Biggar last night replaced Rhys Priestland as the starting fly-half for Wales as they fell to a 26-19 defeat to Samoa, the no.10 going off with a head injury in the first half.
Wales have now lost the first two of their four autumn internationals and face the possibility of falling out of the top eight in the IRB world rankings if Samoa can beat France next week.
Biggar was one of an Ospreys trio to go off injured and add to Wales' already length injury list, Richard Hibbard and Ian Evans joining him on the sidelines but caretaker head coach Rob Howley refused to make any excuses.
"Obviously we'll take guidance from the medical team," said Wales interim coach Rob Howley.
"We've had injuries over the last three, four weeks and when injuries occur it gives you an opportunity to bring players in and test our strength in depth in the team.
"We'll continue to give that opportunity to players through injuries. It's not easy but that's a part of international rugby."
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