Goulding, 27, was happy at the McAlpine Stadium until his agent, Tommy Cunningham, discovered the scrum-half's new, reduced terms for next season.
Cunningham revealed: "Huddersfield have an offer on the table which is substantially less than the money Bobbie was on last season. He's obviously not happy with that situation and believes that, with the deal put to him, he is not central to the Giants plans."
Hudderfield's managing director, Les Coulter, conceded that it is unlikely an improved offer will be made to Goulding and said: "We have been in lengthy negotiations with Bobbie's agent, and it is our belief that our offer reflects his true worth."
Cunningham was due to speak to a "high profile" rugby union club about the matter this afternoon and, with Goulding having played the 15-a-side game as a schoolboy international, he is confident that a deal can be struck which would lead to the ex-Wigan, Leeds and St Helens player switching codes.
Meanwhile, one player definitely leaving Huddersfield is Andrew Tangata- Toa, the Tongan loose forward.
Tangata-Toa and his wife, Justine, were arrested last week and charged with attempting to pervert the course of justice following a road accident in May. The player was immediately suspended by the Giants. The couple were formally cautioned by police on Wednesday morning and will face no further action, but Tangata-Toa has tendered his resignation to the club.
Halifax have placed their unsettled England hooker Paul Rowley on the transfer list for pounds 95,000. Rowley claimed last week he had been frozen out by the Blue Sox and that their new coach, Gary Mercer, had told him that he had no future at the Super League club.
The Blue Sox initially denied those claims, but, after a board meeting, the club's director, Roger Harvey, said: "In view of what was said in a meeting between Gary, Paul Rowley and myself, the board decided it was in the best interests of the club for Rowley to go on the transfer list."
Rowley now seems certain to be linked with a move to Wigan, who have already signed Chris Chester and Gavin Clinch from the Blue Sox this year.
Salford's former England stand-off Steve Blakeley, who has missed the last eight matches with a foot injury, will make his comeback against his old club, Wigan, in Sunday's Super League match at Central Park.
Karl Lovell, Sheffield Eagles' Australian centre, is to appeal against a three-match suspension handed out for a late tackle.
The former Parramatta player, who has never been sent off, was placed on report during his side's ill-tempered 24-6 win at Wakefield on Sunday and referred to the Rugby League's disciplinary committee. He was yesterday found guilty of making a deliberate late strike with his forearm. The appeal will be heard tomorrow.
Richard Darkes, of Oldham, has been banned for four games for a late tackle with his forearm and Jason Hunter, of Swinton, has been suspended for two matches for an attempted head-butt and punch. Both players have also been fined pounds 75.
The organisers of next year's World Cup are exploring the possibility of using Oxford University's rugby union ground at Iffley Road for one of the group matches. The tournament is to be staged at venues throughout the British Isles and France and attention has been switched to the rugby ground after failing to reach an agreement with Oxford United Football Club.
Organisers of the 2000 Lincoln Financial World Cup have secured a deal worth more than pounds 100,000 with James Gilbert Limited to supply balls for next year's 16-nation tournament.
The exclusive World Cup ball will be made available to retail outlets throughout the world, with royalties going to the World Cup company.