Lloris has been ruled out of action for up to eight weeks after suffering a knee injury in the 1-0 win over Manchester City last weekend.
The injury to Tottenham's number one goalkeeper comes at a crucial point in the season, with Champions League football resuming next week and the race for the top four getting tighter.
Forster has played just once in the Premier League since joining Spurs as free agent last summer, with his other three appearances coming in domestic cup competitions.
Stellini has been filling in for Antonio Conte after the former Chelsea manager was required to spend some time on the sidelines to undergo gall bladder surgery.
Conte is due back on the touchline this weekend against Leicester City, and Stellini believes he will have an able deputy to call upon between the sticks.
"We are all disappointed about Hugo" Stellini said.
"But I like Fraser. His behaviour this season has been perfect.
"He trained so hard and in this he also pushed Hugo to train hard.
"We mustn't forget that we have men before we have players and I like Fraser.
"Physically he's perfect for the Premier League and the style we have. He can also use both feet and it will be interesting to see him for the next few weeks."
