The six-year-old is only ‘a possible’ for the Grade Two contest and might wait for the Ascot Handicap Hurdle at the Berkshire track the following Saturday.
The Lambourn handler revealed he only added his charge to the list of runners at Cheltenham after the race was reopened due to insufficient entries on Monday.
“I’m not sure if he runs on Saturday. I put him in when the race reopened. He does have a possible engagement at Ascot the week after, but I will have a look,” said Greatrex.
“I thought it is a possible and maybe if the Irish horse (Laurina) didn’t come over.
“Some of them have been there and done it, whereas he is more unexposed than some.
“I’ll speak to the owners. We’ll see what runs and make a decision.”
Western Ryder made an encouraging seasonal debut when fifth to Nietzsche in the Greatwood Handicap Hurdle at Cheltenham last month. He is a general 20-1 chance to record his first success at Graded level at Cheltenham on Saturday.