The 24-year-old is the subject of interest from several clubs after helping Dale win promotion from League Two, with O'Driscoll waiting to see how things pan out.
He told the Sheffield Star: "We've chatted to Tom Kennedy and he's got two or three other clubs showing an interest, who obviously he'll go and see.
"We've not offered him anything. We've just said to him that we are in the market for a left-back. We told him that we'd watched him two or three times and that he'd fit in with what we do.
"As I say, he's got some big clubs looking at him as well and people have got to decide which is the best move for him."