Leicester are on the lookout for a new manager after Nigel Pearson left for Hull City yesterday and Sousa has been installed as the clear early favourite for the post.
The Portuguese, a good friend of Milan Mandaric, has been strongly linked with a number of jobs over the summer after finishing 7th at Swansea in his first season.
He has been placed at 4/11 to take the Walkers hot seat, with former Reading boss Brendan Rogers the second favourite some way behind at 5/1.
Earlier today, he was at 4/6 and started out at 20/1 when the market opened.
Huw Jenkins refused to confirm what the club's response to an approach would be should Mandaric come calling for Sousa.
"There hasn't been any contact and I have got no idea whether they are interested in Paulo," Jenkins said.
"I am not commenting on speculation. I have had a meeting with Paulo and he is concentrating on Swansea City."
Lee Watts, of Mark Jarvis bookmakers, told the Leicester Mercury: "The word on the street is that Paulo is the man for Milan and that is reflected in his odds."
This article first appeared on JACKARMY.net.