But his return has coincided with a run of three wins in a row, as they begin to climb the league table.
This weekend attention turns to European travails and a clash with Bordeaux-Begles, opposition they beat 19-16 at the Liberty Stadium last Saturday in which Biggar scored all of their points.
But Rees insists Ospreys have strength in their squad beyond the 26-year-old fly-half.
"Dan is a huge influence and we are blessed to have him," said Rees.
"He's the heartbeat of what we do, but I wouldn't say we are over-reliant on him.
"He can't do everything and we shouldn't be asking him to do everything. We have faith in people around him.
"There's Alun Wyn Jones, one of the world's greatest leaders and captains, and others around the group such as Paul James and Justin Tipuric.
"When we get it right, we're firing and we add fluidity to our play, it isn't just about Dan.
"When we are sticky, he steps in and we have to prioritise different parts of our game. He does that and we did enough to win a game last weekend.
"But, to be good, we need everyone on page and being super-good."
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