Allardyce has repeatedly stressed that he will have to sell before he can buy any new players, but the manager indicated that O'Neil could be an option if some money became available.
"We're aware of the availability of Gary O'Neil from Middlesbrough," Allardyce said. "But at the moment we don't have any finances in place to move for any players."
He added: "If that changes and the board tells me there is, then we'll have a look in the market.
"If it doesn't, then we stay with what we've got."
Asked if any player looked set to make way in order to create the necessary funds, Allardyce said: "Not at the moment because we haven't had a bid for anybody.
"We will have to just wait and see what progresses in that area."
Source: PA
Source: PA