Poyet was appointed Brighton manager a couple of months before Brian McDermott got the Reading job and Poyet took the club up as League One Champions ahead of Southampton in 2011.
He signed a new 5-year deal at the club in September of that year so he won't be cheap if we do want him to take the hot seat.
Neither club have confirmed the reports.
We'll have more from this story as it develops.
Now TalkSport are in on the act, exclusively claiming that we've met with former Saints boss Nigel Adkins.