The 35-year-old hit-man emerged as a shock target for the Gunners on the final day of transfer activity, with Arsene Wnger believed to have been searching for central striking reinforcements.
A massive £2m loan fee was offered to the Serie A side to take the German for the remainder of the season, but the Rome club held firm to keep their experienced ace.
It is thought that their actions have saddened Klose, who was desperate to make the move.
The veteran centre-forward is believed to have seen the switch as a great opportunity to boost his chances of a spot in Germany’s World Cup squad, and he was also excited at the prospect of linking up with compatriots such as Mesut Ozil and Lukas Podolski.
Although he wouldn’t have been a regular started at the Emirates Stadium, Klose may well have played a big role in the North Londoners’ push for the title.
It is also speculated that Wenger failed with a late loan move for Newcastle’s Papiss Cisse.