The 2009 European Tour, offering around 140 million euros (£111 million) in prize money, is proving an irresistible lure.
Colombian world number seven and US Tour player Camilo Villegas this week became the latest to say he would consider committing to the mandatory 12 2009 European Tour events - including a minimum two on European soil - to qualify as a member.
World numbers two and three, American Phil Mickelson and Fijian Vijay Singh, have said they may play both tours next season, along with South Africa's Masters champion Trevor Immelman and Australian Robert Allenby.
Several of Europe's top players are set to play less in the United States and more in Europe next season, including world number four and 2008 double major champion Padraig Harrington of Ireland.
The news is music to Bjorn's ears and he feels it will get full support from his members.
"I'm very clear on it: anybody that wants to join this Tour, and that goes all the way through the ranks, they are more than welcome," Bjorn said on Saturday.
"It's a great sign of where our tour's going, that we've made some great decisions. These guys are taking note. They want to be a part of it and that is great. It's going to give a lot of confidence to our executives - that they are doing a very good job."
Bjorn feels an influx of world-class players, like Mickelson and Singh, can only boost the European Tour's standing.
"The US PGA Tour will always have their strong events and strong fields but we are trying to build something and we are going to open our arms to the people who are available," he said.
"We've got to create the strongest fields with the best players available. That's got to be the main objective.
"We've had some tough years when the US PGA Tour's been so strong. A lot of our guys have disappeared over there to play their golf and if it can turn a little bit our way so that some guys are going to come back and some guys, even American guys, are going to come and join, then we've got to say 'thank you very much, things might be turning a little bit in our direction' - and be happy about it."
The Danish chairman is unabashed at the thought that some players might just be 'cherry picking' now that Europe has such a big pot on offer.
"I don't think they are. And when you are the best players in the world you should be allowed to play anywhere you want.
"Professional sport will always be about those at the top. And with the tour we have now, we've created enough playing opportunities to enable everybody on the tour to play when they want.
"When it comes to our big events we want as strong a field as possible. If we get players the likes of Camilo and Phil joining us it's a signal we've sent out that we have something very strong and something people believe in."
Bjorn said steps were taken earlier this month to ensure any player committing to Europe would play a realistic amount of times.
"We made a statement by going to a mandatory 12 events (to qualify as a member). We said we want you to be members of our Tour, but want you to be participating as fully as possible. That's why we went to 12.
"The guys I've talked to who are considering playing over here, it seems to me it doesn't deter them at all. They do want to be a part of the Tour."