Beckett 29, looks set to leave Bramall Lane after limited opportunities and a very successful seasons long loan spell at Boundary Park but despite agreeing a £100,000 deal the Latics are having problems agreeing terms with the player.
The former Barnsley striker netted six goals in seven league games for Huddersfield Town in a loan spell in January 2005.
"Luke is a player we would be very interested in, but we understand Oldham have an option on him until mid-June," said Peter Jackson, Huddersfield Town manager.
"Nothing can be done until that option is either exercised or lapses, which is why we haven't been in a position to push anything at this stage.
"Should he become an option then we would have to look at the whole financial package. He is a quality striker."
It is believed that Bradford City are also interested in Beckett, they believe he would make the perfect strike partner alongside Dean Windass.