The Foxes are searching for a new boss following Nigel Pearson's defection to Hull last week and are understood to have agreed a compensation package with Swansea for ex-QPR manager Sousa's services.
A statement from Leicester read: "Following his release by mutual consent with Swansea City FC, Leicester City confirm that they have initiated talks with Paulo Sousa in regards to the vacant manager's job.
"Further updates will be provided in due course."