Danny Green currently fights in the cruiserweight division and he is ranked 7th in the world by The Ring Magazine: the majority of the fighters who are ranked above him are European fighters who typically fight in Europe, so if he wants to fight them, he should go to wherever they are located and challenge them, since they have paid their dues at cruiserweight while Green's only notable win at that weight is a knockout over a faded Roy Jones. You mention Antonio Tarver but Tarver is a light heavyweight, which is 175 pounds and Green struggled to make the 180 pound catch-weight for the Jones fight. If Green wants to fight Taver, he should have to come here and fight him because Tarver knocked out a much younger and fresher version of Jones and regardless it looks as though Tarver may not fight again. But as far as cruiserweight goes, here are the 6 fighters ranked above him and what the chances are that they could face Green:
~ Troy Ross (number 6 rated contender)- Ross has nothing scheduled at the moment but he doesn't really bring anything to the table for a Green fight since he is not a world titlist. Ross does have some fame since he won the fourth season of the boxing reality series The Contender, so the fight may happen since Ross fought his fights on The Contender in Singapore, which is relatively close to Australia and both are known fighters there but as stated, Ross doesn't bring anything to the table.
~ Giacobbe Fragomeni (number 5 rated contender)- Fragomeni will be facing Krzysztof Wlodarczykin a rematch in an attempt to win his old title back that he lost when he fought Zsolt Erdei- the Wlodarczyk fight will be for the vacant WBC cruiserweight title. If Fragomeni can regain his title, a fight with Green is certainly possible since it would be a title fight but Green would be obligated to face Fragomeni where he is based, not the other way around.
~ Marco Huck (number 4 rated contender)- Huck just defended his WBO title this past weekend, so he'll be out for a little while. If Green wants to challenge Huck for his title, he'll be obligated to fight wherever Huck wants to fight.
~ Zsolt Erdei (number 3 rated contender)- Erdie beat Fragomeni for his WBC title but since Erdei is moving back down to light heavyweight, Fragomeni will fight Wlodarczyk for the vacant title and since Erdei will no longer be fighting at cruiserweight, a fight with Green is out of the question.
~ Krzysztof Wlodarczyk (number 2 rated contender)- as previously stated, Wlodarczyk will be facing Fragomeni in a rematch of their draw for the vacant WBC title. If Wlodarczyk wins, Green would be obligated to face him wherever Wlodarczyk wants since the latter will be the one with the world title.
~ Steve Cunningham (number 1 rated contender)- Cunningham will be facing Matt Godfrey (number 8 rated contender) for the vacant IBF title in the near future and I think Cunningham would be willing to travel to Australia to fight Green because Cunningham has fought in many foreign countries in the past, even when he was the defending champ.