The Everton Under-23s coach could still be on the move despite rejecting Oxford United this week.
Unsworth is reported to have turned down a move to Oxford United this week, but remains on the bookmakers' list of candidates for the Barnsley and Bradford positions. However, there is no suggestion at this stage that the 44-year-old has been contacted about either role.
A renowned youth coach, Unsworth had a hand in developing young Everton talents such as Tom Davies, Dominic Calvert-Lewin and Jonjoe Kenny.
He also led Everton's youngsters to the Premier League 2 title last season and later had a spell as Toffees caretaker manager.
Only seven points separate sixth-placed Bradford and tenth-placed Oxford United in England's third tier, and the former club's location - accessible by the M62 motorway which begins in Liverpool and links to the M61, serving Unsworth's native Chorley - could explain the 44-year-old's interest in that role over the other.
Unsworth is already familiar with the Yorkshire region, having had spells at Sheffield United and Huddersfield Town.
Can Everton afford to lose Unsworth?