The Mirror says Inter have warned they are ready to walk away from a deal for Sturridge.
The Liverpool striker had been linked with a loan move to the San Siro after falling out of favour at Anfield.
Liverpool had slashed their proposed loan fee from £5m to £1.5m after failing to attract any offers.
Inter remain interested but sporting director Piero Ausilio has suggested a deal isn't close.
“Sturridge? I don't exclude anything, but we made our evaluations," he said. “We already have players for that role."