O'Neill, however, does not expect the 29-year-old to miss the World Cup qualifier in San Marino on September 1 regardless of who he is playing for when the transfer deadline closes.
"I know Jonny's level of professionalism will mean he won't be distracted by the whole thing," O'Neill told Sky Sports News.
"Ideally if it's suitable for all parties and it can be agreed the sooner it can be done the better in terms of our preparation. Sometimes these things take time. They can go right to the last minute.
"But he's played at the biggest club in the world since he was 18 or 19 and won the Premier League on three occasions [with Manchester United] so he's vast experience of what is needed to play at a big club."
Evans missed West Brom's unbeaten start to the Premier League season with a hamstring injury.