Radamel Falcao has played down talk of a summer move to Juventus and says he is fully focused on Manchester United.
Cranie is available on a free transfer after rejecting a new deal at Coventry and he has spent the past fortnight training with Leeds.
The former England Under-21 international, who can play at centre-half and left-back, has shown enough to warrant Warnock to follow up his interest.
Warnock will now hold talks with the 25-year-old to see whether Cranie is prepared to accept the role he has in mind for him at Elland Road.
"He's a steady player and what I'd call a squad player," said Warnock in the Yorkshire Evening Post.
"Where it goes from here really depends on what Martin's looking for and what we can afford to offer him.
"He's calm, collected and a good lad who's fitted in well with the other players. We just need to chat things over and see what happens."