The Reds, already the home of the likes of Will Genia and Quade Cooper, are said to be the favourites to capture his signing. But Perth-based Western Force are desperate to hold on to one of their brightest stars.
O'Connor, whose late try and conversion last October helped Australia to a first win over the All Blacks in 11 attempts, will make a decision this week.
"I haven't made a decision yet, but it'll be a footy decision," said O'Connor.
"This is the time-frame I wanted to look at, this week. Until now I just wanted to focus on football.
"But now I will just go through everything and see who is going to be best for me."