The seven-year-old is as big as 33-1 with some bookmakers for the Grade One contest over two and a half miles, which the Wantage trainer thinks is generous.
Bigmartre has solid form going into the Festival. After beginning his career over fences with victories in novice events at Ludlow and Newbury, he was only narrowly beaten by seasoned campaigner Duke Of Navan at Doncaster.
"He's going for the JLT. I think he's quite a big price," said Whittington.
"At Doncaster he hated the sticky ground and it looked to Harry (Bannister, jockey) that now is the turn to step up. We always thought he would improve for going up to two and a half miles.
"He races in a very relaxed manner and the bigger the jumping test, the more important it is for him.
"He is very good for a novice. His jumping is outstanding.
"We want to give it a go and we think he's earned the right.
"Taking on older handicappers at Doncaster, he almost pulled it off. It was a head-bob. And he thinks he's won.
"He probably should be unbeaten going into the JLT. He beat Cyrname at Newbury so he's very much entitled to go there."
Select any odd to add a bet