The six-year-old, trained by Stephen Gray, is among the outsiders for the six-furlong Group One on Saturday week.
But given the record of overseas sprinters down the years, he should not be written off.
Gray said: “He has been a bit agitated, but that is only because it is all new. The weather is a bit different to what he is used to, but he seems fine with it now.
“At home he is in a big barn and the horse is used to be in a confined space. He is enjoying the open space on the training grounds and looking out of his door.
“The trip over will have been like a race for him, and we have just got to keep him ticking over and keeping him healthy. He had a blood test last night, and it was good. I was happy out with him on the gallops this morning.”
On his last outing Lim’s Cruiser finished second to Bold Thruster at Kranji, his first run since not being disgraced in the Hong Kong Sprint.
“I was umming and ahhing about coming. There was nothing at home for him, and Mr Lim (owner) said ‘go have a crack at it’ – so we have to thank him for that,” said Gray.
“If he turned up at his best he would run very well. If the race was in Singapore he would have been extremely hard to beat. It is hard to win the race here, let alone having had to travel as well.
“There are another couple of races for him after this, the July Cup at Newmarket and Lennox Stakes (Goodwood).
“If he finished in the first three or won it he might get a slot in the Everest (in Australia). You have got to have dreams!”
Gray said: “Emperor Max was a different type of horse. He was a bleeder, and that stopped him from being a superstar.
“I learnt a lot from that trip here with him and learnt that we can compete. A lot of it is down to having the nerve to have a go at it. If you turn up and try your best sometimes dreams come true.”