The former Manchester United captain is also looking at Wigan's Nathan Ellington and Ipswich marksman Darren Bent as Danish flop Jesper Gronkjaer has all but sealed his £1.5m move to Atletico Madrid.
But David O'Leary is also in the hunt for Deano, as Everton look likely to sign James Beattie, O'Leary's long-term striking target. The ex-Leeds boss reportedly sees Ashton as an excellent alternative.
There are also reports that Liverpool, Crystal Palace and Charlton Athletic are interested in the 21-year-old.