The Italian international centre back is highly rated and the North London side will have to fight off interest from Juventus, AC Milan and Fiorentina.
Liverpool were also rumoured to have been scouting the 24 year old who is expected to go on and become a top defender.
Champions League football will be key for Arsenal if they are to get their man and so Ogbonna is expected to wait until the end of the season before making a decision on his future.
The Turin club want at least £17million for their main man and so the Italian clubs have quietened their interest leaving Arsenal as the favourites to snap him up.
Wenger has a large budget to spend in the summer to finally get Arsenal back in the title race for next season.