Hartnell remains in the mix for the Melbourne Cup but trainer James Cummings has not committed last year's third placegetter to a start.
After being taken out of several betting markets, Hartnell has been reinstated after Godolphin paid up at the latest acceptance stage on Monday.
The stable had indicated the $2 million Emirates Stakes (2000m) on Saturday week would be Hartnell's next race.
He pleased Cummings in a course proper gallop at Flemington on Tuesday and the trainer said there was a strong chance he could line up in next Tuesday's Cup (3200m).
"We nominated for the Cup at the very beginning of the spring and it had always been high up on our agenda," Cummings said.
"But the more that the spring unfolded and we could see how everything was piecing together, the more we felt like it looks like a nice fit for the horse.
"But no final decision has been made just yet."
He said that was likely to be made by Thursday or Friday.
"The horse is owned by His Highness Sheikh Mohammed and if he wishes to run the horse elsewhere then that's his prerogative," Cummings said.
"But we're happy with the way the horse is going. And if everybody is on the same page then he looks like running in the race."
Hartnell finished 15th in the 2015 Melbourne Cup and started favourite last year when trained by John O'Shea.
He carried 56.5kg in 2016 and would be top weight with 57.5kg this year.
Damian Lane will ride Hartnell if he runs.
"He looks to be working nicely towards a peak and if it happens that we run him in the Cup on Tuesday, I'm sure he'll acquit himself very well," Cummings said.
The possibility champion Winx might run in the Emirates Stakes could also have a bearing, given she has beaten Hartnell every time they've met.
"The reality is he (Hartnell) has had his chance against her when he was younger and in great form," Cummings said.
"So that option doesn't attract me."
Hartnell has not raced since finishing unplaced in the Caulfield Stakes on October 14 and Cummings said the gelding had appreciated a few easy weeks.
"He'd be an interesting runner if we did run him in the Cup from the perspective that he would go into the race a little bit more on the fresh side," he said.