The Cherries goalkeeper has been in demand heading into the final stretch of the transfer window and the arrival of Kepa at the club pushed him further down the pecking order.
Palace and Luton are amongst the clubs to have been interested in signing Travers.
The shot-stopper will not be moving though as Bournemouth have agreed to loan Neto to Arsenal.
That means they will not be able to let Travers go and he will remain at Dean Court beyond the closure of the transfer window.
Neto is expected to have a medical with Arsenal later today before sealing a loan move to the Gunners for the season.
Arsenal have acted due to agreeing to sell Aaron Ramsdale to Southampton.
Travers came through the youth set-up at Bournemouth and has had loan stints with Weymouth, Swindon Town and Stoke City.
He must now wait until January for his next chance to move.
