The 39-year-old will be out of contract at the KCOM Stadium following Sunday's clash with Tottenham Hotspur, having only agreed a short-term deal when taking charge in January.
Despite failing to keep the Tigers in the top flight, Silva is reportedly on the radar of a number of Premier League clubs - Southampton and Watford among them - and is currently weighing up his future.
Silva has yet to rule out remaining on Humberside for another year to help the club return to the top flight, with further discussions planned once the season is over.
"We started to talk. We will have one more meeting next week, and then we will announce for everyone what the decision is," he told reporters. "The talks were positive. Always when we talk it's positive. As a manager I will analyse, the club as well, and the most important thing is to understand why these things happened, and next time don't make the same mistakes.
"We'll see what happens. First the club looks at what is best for the club. Then me, as a manager, and the players, what is best for the career. Then if we need to talk to the chairman more, we will come up with the best solution.
"It's impossible for me to talk about other clubs. Hull City deserve all my respect. We have one more game to play. It's been a hard week, but we want to try to finish the season well."
Silva has taken 21 points from his 17 games in charge, compared to the 12 points collected in 20 games prior to his appointment.