Jermain Taylor says Joe Calzaghe will need to more than double his purse offer to arrange a fight.
Taylor is the sort of big name American Calzaghe craves
Promoter Frank Warren has offered the middleweight king $4m for a shot at Calzaghe's WBO super middleweight title in the UK in September.
"If Joe and Frank want me that much, make me an offer for $10m and I will show up and bring him a gift to his front door," Taylor told BBC Sport.
Taylor defends his WBC and WBO titles against Cory Spinks on 19 May.
The 28-year-old Little Rock man, who holds a record of 26-0-1 (17 KOs), is refusing to contemplate a Calzaghe bout before then.
Joe only wants to fight the best man out there and that is Jermain
But he says that if the money was right he would move up to super middleweight, and he would not have a problem with fighting in the UK.
"No atmosphere is intimidating because once you start fighting your focus is on the man in front of you," said Taylor in a question and answer session for the BBC Sport website.
Calzaghe, 35, made the 20th defence of the title he has held for 10 years against Peter Manfredo Jr on 7 April in front of 35,000 fans at Cardiff's Millennium Stadium.
He hoped to be in action again on 21 July, but a broken hand suffered against Manfredo and the lack of a suitable opponent looks likely to delay that until later in the year.
"Joe only wants to fight the best man out there and that is Jermain," said Warren last week, after offering Taylor an American referee for a potential bout.
"I know Jermain wants to fight only the biggest fights and make the most money.
"To do that we need to hold the fight over here where we can build on the record attendance Joe established against Manfredo."
Calzaghe says he should be over a broken hand by July
Bernard Hopkins and WBC and WBA super middleweight champion Mikkel Kessler are unavailable in July, though the latter's camp have said that they would be willing to fight Calzaghe in the UK in September.
Unbeaten British and Commonwealth super middleweight champion Carl Froch also says he is keen to take on the Welshman.
But the Nottingham fighter is little-known to the US TV audience and Warren claims that he has refused large purse offers for a bout.
Roy Jones Jr says he is ready to meet Calzaghe anytime, anywhere, but previous negotiations between the former four-weight title holder and Warren have collapsed over money.
That could leave WBO mandatory challenger Denis Inkin as a potential opponent.
The German-based Russian, 29, holds a record of 30-0 (23 KOs) including wins over Calzaghe-victims Branko Sobot and Mario Veit, but he is an unknown in the UK and USA.