The Irish star damaged his right ankle on international duty last week.
He has already missed the games against his former club Leeds and Liverpool and the ligament problem will keep him out of Saturday's clash against Fulham plus Ireland's key Euro 2004 qualifiers next weekend.
Glenn revealed this afternoon: "It's encouraging news although we won't know until we have another observation about a week down the line.
"The swelling has gone completely down and the bruising is coming out. There is a ligament strain in there, for sure, but Robbie is a quick healer and I'd say after the next 10 days of treatment we might have a better picture of when he'll be back."
Glenn Hoddle says the news is 'encouraging' on Robbie Keane's recovery from an ankle injury.