Chief executive Tony Ball has told City analysts he is prepared to drop what he terms "lesser" competitions when the rights come up for renegotiation next summer.
He has made it clear to the City that major sports rights like the Premier League, which in 2000 Sky paid £1.1billion for, remain central to Sky's future.
A Sky spokesman said today: "We are going to be careful with the rights we choose and careful about what we pay."
The first sign of Sky's new approach came last week when it dropped its Six Nations rugby deal to concentrate on England's autumn internationals against South Africa, New Zealand and Australia.
There's no suggestion Sky will try to break its FA contract, but Ball has made it clear he is no longer prepared to pay millions for rights which are not bringing in mass audiences.