Bernard Dunne's camp have been advised that they will have to put in a higher bid if they want Esham Pickering to fight in Dublin.
Both men have been nominated by European Boxing Union (EBU) chiefs to box for the vacant European super bantamweight title.
But the fight has been left open to purse bids on 11 October in Rome at 12 noon (Italian time).
Bernard Dunne's manager Brian Peters confirmed yesterday that he had made a private bid to Pickering's camp on Wednesday to try and entice the Englishman to Dublin.
But Pickering's manager, John Ingle, said yesterday that Junior Witter's promoter Mick Hennessey, who appears to have the backing of Sky Sports, are willing to pay a higher amount.
Ingle, whose Dublin born father Brian, is coaching Pickering, also indicated that Ricky Hatton's promoter Denis Hobson, is also interested.
He said, 'We will take the best offer and that is the bottom line. We have received a private bid from Brian Peters this week.
'But Mick Hennessey says he is willing to make a better offer and if Brian Peters wants to come back to us then we will obviously listen to what he has to say.
He added: 'Esham would have no problem coming to Dublin to fight Bernard Dunne as long as the purse is right.'
Brian Peters said he believed that the private bid he made Pickering was 30% more than any offer the puncher had received in his career so far.
However, Dunne's manager now appears resigned to travelling to Rome next month to put in his purse bid at EBU offices.
Peters said: 'I will go to Rome next month and put in our bid and take it from there. I made a private offer to Esham Pickering's people this week but it looks like it is going to purse bids.'
Unbeaten Dunne, who has won his 21 fights so far, and Pickering, who has lost four 4 from 33, were nominated by the EBU after reigning European champ Michael Hunter this month relinquished his crown to concentrate on a world title tilt.
Hunter was dropped twice by Pickering in a European title fight in 2005, but got up to win the decider.
