Albion made initial contact with the out-of-work Ranieri two weeks ago and followed up their interest by holding a second round of talks with the Italian in London on Thursday.
Ranieri met with Albion chairman Jeremy Peace and the club's sporting and technical director, Dan Ashworth.
He is an attractive possibility as he will not cost West Brom anything in compensation.
However, sources close to Albion stress the additional talks do not mean Ranieri will automatically be offered the post made vacant after Hodgson was appointed England's head coach.
It is understood the Baggies have also made contact with former Chelsea and Manchester United midfielder Ray Wilkins.
But Birmingham boss Chris Hughton remains high on the list of the candidates who appeal to Peace although no formal approach has yet been made to Blues.
Hughton came close to replacing Roberto Di Matteo 15 months ago after being interviewed by Albion before Hodgson took up the post.