The 10-year-old has now won back-to-back races this season after he followed up his Aintree win with a solid display at Newbury on Saturday.
Broom’s ace is set for another crack at the Gold Cup at the Cheltenham Festival next month but a run in the National against Tiger Roll is now unlikely.
The two market leaders may drop out of the race at Aintree, with Gigginstown House Stud claiming they are unhappy with the mark of 170 for two-time winner Tiger Roll.
Native River is as big as 14/1 to win the feature race, and with a mark of 166 he has a chance, but Broom says it is unlikely he will run at Aintree if he competes at The Festival.
He told the Racing Post: ‘We are not ruling it out completely, but I think it’s unlikely and I wouldn’t go saying anyone should back him for the Grand National until after the Gold Cup.
‘I think he has been dealt with fairly and have no complaints about his weight – I think it’s very reasonable.
‘We have to get the Gold Cup over first and see how he comes out of it.
If he puts everything into the Gold Cup as he has done before, then, if you look, he has not run again after his Gold Cup efforts.’
Contingencies to re-stage if Cheltenham were postponed ‘for any reason’.
Doncaster and Newbury options for Towton faller.
Trainer took a batch of 13 horses to work on Tuesday morning.