Over the past three years, Tsonga has chosen not to play in the week before the Australian Open, either coming to Melbourne directly or via the multi-million dollar event in Doha.
However, in 2008, Tsonga played both the Brisbane and Sydney events (which were the same level as the Heineken Open) as a precursor to the grand slam. In 2009, he competed in Adelaide and Sydney before coming to the Australian Open.
"We'd love to see Jo here," says Heineken Open tournament director Karl Budge. "He is an incredible talent. He has a lot of personality and a lot of charisma and he would relate to New Zealand fans brilliantly. He has a big presence and wouldn't look out of place in the All Blacks back row.
"We chatted to him in New York and we will continue those discussions. He is of interest to us and will continue to be because he would be massive here."
Budge admits that Tsonga comes with a big price tag but is not ruling out the possibility.
"I think our chances are as good as anyone else," says Budge. "He's a player that has often played that week and that helps. It would be great to see someone of his calibre down here. He is also one of the few guys that can do a lot of your marketing for you. But he has been in demand in this region for a number of years and can afford to shop around. He knows that if he turns up, there will be bums on seats and you have to pay for that privilege."
If Tsonga would be an unlikely coup, Budge also raised the possibility of Roger Federer being seen again in Auckland, after his first round exit here (he lost in straight sets to Juan Carlos Ferrero) in 2000.
Budge met with Federer and his representatives in New York during the recent US Open and feels the door is not closed on the Swiss returning to New Zealand in the future.
"I've love to see Roger here at some point," says Budge. "Roger indicated to me that he has another four or five years in him - which was quite interesting - and we are the only tournament that he has played in that he has never won a match at. He likes his stats and I certainly reminded him of that."
Federer would be the longest of long shots for the future but he has said in the past that "everything depends on his schedule".
Meanwhile, three time champion Ferrer is again on the radar for 2013 while Auckland Tennis are also in discussion with 2009 winner Del Potro.
"There is a group of five or six players that you enter into discussions with as soon as you possibly can," says Budge, "and you hope to get one of them across the line."
Budge expects to have signed his top names by mid-October, with the first player announcements to follow shortly after that.
