The Hoops midfielder has been sidelined with a hamstring injury he sustained in pre-season but is a chance to return in the weekend's home meeting with Aberdeen.
The Scottish champions currently sit fifth on the league table after four matches and Deila is eager for the influential Brown to play some part in the Parkhead fixture against the 8th-placed Dons.
"He is training well so he could maybe play on Saturday," said Deila. "We will see.
"Everybody knows how important Brown is for Celtic. He is the leader, a person who demands things and shows the way.
"He is going to be a huge player to get back on the pitch. He is very happy and has had fantastic training today."
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