Marco Silva is in Portugal to hold talks with Porto about their vacant manager's job, according to Sky sources.
Silva, who has a relegation release clause in the Hull deal he signed in January, said at the weekend he expected to make a decision on his future by Wednesday.
Porto have since parted company with boss Nuno Espirito Santo, and it is understood former Sporting manager Silva is now discussing a return to Portugal.
The 39-year-old was unable to save Hull from relegation after replacing Mike Phelan, but six home wins in the Premier League kept them alive until the penultimate game.
The club's supporters chanted for Silva to stay throughout a 7-1 defeat to Tottenham on the final day, but he said after the game: "I need to think and see what is the best solution, not only for the club, but for me as a coach and for my career.
"I need to decide. The club needs to know and start to do things differently to last summer. It's clear that you start to win or lose with everything you do in the summer when you prepare the season and the team.
"I am sure next Wednesday we will decide."