The unbeaten four-year-old made a seamless switch up to 10 furlongs in the Juddmonte International Stakes at York, beating Mishriff by six and a half lengths on what was his first start beyond a mile.
Connections had previously stated their intention to head directly to Ascot for the Qipco Champion Stakes on October 15 for Baaeed's career swansong, but trainer William Haggas then raised the possibility of a trip to Ireland while a further step up to 12 furlongs in the Prix de l'Arc de Triomphe on October 2 was not ruled out.
However, Sheikha Hissa, who now heads the Shadwell operation established by her father Sheikh Hamdan al Maktoum, has decided the son of Sea The Stars should have just one final run before retirement, ruling out a trip to Leopardstown and making supplementary entry for the Arc a live possibility.
Shadwell's racing manager Angus Gold said: "He is not going to run in the Irish Champion. Sheikha Hissa said she and the family wanted to have one more run, either in the Arc or the Champion Stakes.
"It would be lovely for anyone to have an Arc winner, of course it would be wonderful, but equally it would be wonderful to have a Champion Stakes winner.
"He is a very good horse, so let's hope wherever he goes, whatever everyone decides, that he can maintain it."
Baaeed is not currently entered for the Arc and would have to supplemented at a cost of €120,000 on September 28 if he were to make a further step up in distance, with both conditions and possible rivals crucial considerations in Gold's view.
"There is no rush to make the call. We don't have to technically supplement him, if we decide to go for the Arc, until September 28," he said.
"Let's see what the weather does to us in the next month or so and see what is running in the Arc and everything.
"If we get a wet autumn - and who knows - but if we get a wet autumn and it was going to be heavy ground in Paris, then it would be less likely. Equally, it could be very heavy ground at Ascot.
"How many runners in the Arc would also come into the calculations (because of the potential of a bad draw)."
Reflecting on his International victory at York, Gold added: "It was lovely to see him win so well at York.
"There was so much hype about was he going to stay or wasn't he going to stay and if William didn't think he wouldn't, we wouldn't have thought about it. I thought he would stay since he ran his first race.
"It was nice to see him win it, but win it so dominantly and give such an impressive display and show what he really can do.
"He is never going to surpass Frankel because he didn't win as a two-year-old and didn't win a Guineas. Frankel is Frankel and Baaeed is Baaeed. Both are outstanding horses and we are just very lucky to have him. That is really all that matters and it is only people's subjective opinion."
Baaeed has banked six Group One wins on the spin now, with his neck verdict over Palace Pier in last year's QEII Stakes at Ascot his narrowest margin of victory.
Gold admits he would be thrilled if the colt, who is a full brother to Coronation Cup hero Hukum, could bow out unbeaten but feels the 135-rated Baaeed has little left to prove now.
He added: "I think the important thing from our point of view is what happened last week, because that showed him now to be an outstanding horse. Before everybody was questioning him, saying he hasn't beaten anything. To be fair, John Gosden said he has always looked like he was crying out for further, which you didn't have to be Einstein to work out.
"How vital is it he remains unbeaten? It is not vital he wins an Arc, it is not vital he wins a Champion. He is brilliant horse and is the best horse around and that is all that matters. Of course, anything else now is a bonus.
"For me, the Arc is the greatest horse-race in the world, always has been and always will be in my lifetime. Of course, it would be nice to win it, but he is no lesser horse if he doesn't win an Arc.
"We have seen what he can do over the last 16 months and we know he is a very good horse and luckily he has now shown that to the world at York. Anything else is a bonus."
Haggas thinks there is a "strong chance" Baaeed will line up in the Arc, if conditions are suitable.
He told Sky Sports Racing: "Obviously, he is not in the Arc so will need to be supplemented but we are not keen to run him on bad ground in Paris, so if the ground is nice, there is a strong chance he'll go there.
"Otherwise, he'll wait for the Champion Stakes and run there whatever."