Relegation-threatened Livorno have sacked Domenico Di Carlo after just 88 days in charge and re-appointed Davide Nicola.
Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
Navarro joined the Seagulls from MK Dons in 2009 and has made 85 appearances, helping the club to promotion to the Championship last season.
Boss Gus Poyet told the club's website: "Alan has had an exceptional season and proved himself at this level but we are very well covered in that position.
"With that in mind it was difficult to offer him another contract, but I am sure he will have no shortage of offers."
Poke has made one senior appearance for Albion and spent the second half of the season on loan with Bristol Rovers.
Gonzalez has played twice for the first team after joining on a short-term deal from Manchester City in January.