Jason is currently working as Strictly’s chief choreographer but has now been tipped to take up a role as a judge.
Len confirmed before the last series that the 2016 show would be his last on British TV.
Len said: “In 2004, I was asked to take part in a brand new BBC Saturday night show and who would have thought me, old Len Goodman, would still be part of this amazing series more than 10 years on.
"This adventure began when I was 60 and now that I’ve reached my 70s, I’ve decided after this year it’s time to hand the role of Head Judge to someone else."
He added: "It is an honour being part of the wonderful Strictly Come Dancing family and I’m looking forward to my last series very much and to whatever comes next.”
A number of names have been rumoured for Len's job, mainly pro dancers including Anton Du Beke, Brendan Cole and Karen Hardy.
But the Daily Mail newspaper now report that Jason is a frontrunner to takeover from Len.
As well as his work on Strictly on BBC one, show bosses have also apparently been impressed by his judging on Aussie TV series So You Think You Can Dance as well as his credits on the US version of Strictly, Dancing with the Stars.
A source told the newspaper: "Jason is viewed as a perfect replacement for Len.
"He is being described as a really, really good call by some of the most influential and professional dancers on the show. He is their choice."
Strictly Come Dancing will be back on BBC One later this year for its brand new series.