The Chilean, who is on a year-long deal at San Siro, has been ruled out for the rest of the year after undergoing ankle surgery.
Inter spent big on bringing in Romelu Lukaku from Old Trafford over the summer but could dip their toes into the English market once again to strengthen their attack, according to Calciomercato.
Antonio Conte’s side failed in their efforts to sign Roma’s Edin Dzeko and a suitable alternative to Lukaku is now a priority.
Tammy Abraham’s emergence has limited the 33-year-old’s chances and Inter hope to capitalise on his desire for more regular game time.
Giroud will not want to risk losing a place in the France squad for next summer’s European Championship.
The Serie A side believe that Giroud’s blend of technical and physical qualities would make him an ideal partner for Lukaku.
However, he wouldn’t be guaranteed a starting spot in Milan either after an impressive start to the season by Lautaro Martinez.
The 22-year-old has scored three goals in nine games across all competitions for Conte’s side, the same number Lukaku has notched so far.
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