Hulse turned down Stoke City last week after the club agreed a £1.2m fee with the Baggies.
He was also linked with Burnley as part of the deal which took former Leeds target Richard Chaplow to the Hawthorns on Monday.
Hulse cost £750k when he left Crewe in 2003 and West Brom would be keen to get that back if he agrees a transfer elsewhere.
Hulse's agent Steven Hughes refused to confirm Leeds' interest but said: "Leeds are the type of team that Rob would look for. He would want to join a club of that size with that quality of players, but above all he wants to play football. He's not getting that chance with West Brom even though he was their top scorer last season."