After missing out on Lazio's veteran Germany striker Miroslav Klose the Gunners turned their attention to the Juventus forward, but he was unwilling to join on loan.
Juventus was willing to sanction a loan deal for the Montengrin but the player turned down the chance to move to the Emirates Stadium.
Vucinic was not interested in a loan switch and only wanted a permanent transfer to Arsenal or Tottenham, which also expressed an interest in the 30-year-old.
The former Roma man is settled in Turin and did not want to upset his family life midway through the season.
Arsenal is believed to have made an attempt to sign Vucinic after failing to sign veteran German striker Miroslav Klose from Lazio, as revealed by Goal earlier on Friday.
Vucinic has found himself way down the pecking order at the Serie A leader, which added another striker to its squad on deadline day when it signed Southampton outcast Dani Osvaldo.
Vucinic will compete with Osvaldo, Carlos Tevez, Fernando Llorente and Fabio Quagliarella for a place in the side.