Gerrard signed the 34-year-old on loan in January after he fell out of favour at St. Mary's.
The Northern Ireland international has slotted neatly back into the Rangers side, featuring in the majority of their games.
“I think he will be here next season," said Gerrard. “At this moment, we cannot confirm he will be here.
"But I want a fit and hungry Steven Davis in my squad."
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