Reports in Italy carried by talkSPORT claim that the Gunners made a tentative approach for the Danish under-21 star. Arsene Wenger enquired into his availability, initially looking for a loan switch with a further option to buy.
But Inter Milan turned down the proposal with Olsen earmarked as one of the Italian club's future stars.
That hasn't deterred Arsenal though, with club scouts monitoring his progress at the San Siro.
Inter Milan won the race to sign Olsen from Brøndby last year, after he impressed at the 2011 European under-17 Championship with the Danish team.
UEFA picked him out as one to watch after the tournament, and Olsen has gone on to win two caps for the Denmark under-21 team.
The report claims Arsenal didn't make a formal offer to Inter Milan, but the north London club remain interested.
And they'll continue to track his progress ahead of a possible move in the January transfer window.