Sunderland, Fulham battle for Barnsley fullback Stones
Wigan Athletic are also waiting in the wings, says the People.
O'Neill made a surprise £2m move for the England youth cap and wants him to fill a gap in his squad in the next few days.
The Black Cats' bid has topped Fulham's latest offer of £1.7m, with Martin Jol keen to land the top prospect before the window shuts.
Wigan are waiting until a fee is fixed, with boss Roberto Martinez not willing to pay the £3m valuation but interested if the price drops.