The gelding also holds an alternative Cheltenham Festival engagement in the Coral Cup, but is unlikely to take in that contest either as connections consider other options.
After rising considerably in the weights last year, Ross River was well beaten when reverting to hurdling in the Pierse Hurdle at Leopardstown in January and has enjoyed a break since.
“Ross River is highly unlikely to go but if he is to run in anything at Cheltenham then it’d probably be the Coral Cup,” explained handler Tony Martin.
“I think he needs a bit more time really but hopefully we’ll be looking towards Punchestown with him.
“I’d be rushing against time with him and I don’t think I’d have him quite fit enough so it’s unlikely he’ll go to Cheltenham.
“I’d probably need another fortnight with him and he needs another couple of bits of work to be at his best really.
“He went up an awful lot in the weights for winning last year and went for the Mildmay (Racing Post Plate).
“I thought he’d have a great chance there but he’s 15lb higher this year than he was last year.”
Another inmate of the Martin stable, Robin Du Bois, is to be given a break and will not line up at Cheltenham .
Having scored over timber in France last year, the gelding found only Triumph favourite Lounaos too strong on his Irish debut before failing to run to the same level last time.
Of the four-year-old, Martin said: “He’s definitely out and he won’t be travelling.
“Everything’s OK apart from just having some niggly things work against him.
“He’s having a break at the moment and it’s doubtful he’ll go to Aintree either as I think he’ll need a while off.
“We might, if we’re fortunate, be able to get him back for one of our meetings like Punchestown.”
Elsewhere, connections of Labelthou are expected to decide today which race the mare will go for at next week’s Cheltenham Festival.
Having ruled out the Coral Cupaving ruled out the Coral Cup, the remaining two options for the mud-loving eight-year-old are the Ladbrokes World Hurdle or the Brit Insurance Novices’ Hurdle, both over three miles.
“The ground will definitely be part of the decision-making process on which way we go on. It looks like it’s going to be soft which is super,” said trainer Emma Lavelle.
“She seems, touch wood, in very good form and she’ll probably be my only runner at the Festival.”