The 19-year-old only joined the Nerazzurri last summer from Brondby, but he has since caught the eye of Arsenal scouts while playing at youth level.
Having received glowing reports from his scouting team, Arsene Wenger is keen to lure the midfielder to the Emirates.
The Gunners have already offered to take the player on loan with an option to buy, but their proposal was swiftly rejected by the Italian side.
They, nonetheless, continue to monitor Olsen’s development, hoping to snatch him at the earliest opportunity.
The talented footballer has yet to be handed a senior debut at Inter, although he has made the bench in four Serie A fixtures.
Olsen is regarded an important member of Denmark Under-21 side, and has so far made two appearances in the 2015 European Championship qualifying campaign.