NAIJ.com reports that Terry has won 14 major honours with the club including a Champions League title, four Premier League titles, one Europa League title, three League cups and five FA cups.
West Bromwich Albion have been linked with a move for the 36-year-old, and according to the Daily Star, they will face competition from Swansea should the Welsh club remain in the Premier League.
Having made 713 appearances since his debut in 1998 - 578 of them as captain - Terry's departure will certainly leave a big void in the team to fill, but aside from that Neville believes the timing is rather poor from Chelsea.
Terry is thought to be keen on helping the club win the Premier League, even if it is from the sidelines, and of course Chelsea have a huge game in the FA Cup against Tottenham Hotspur this weekend as well.
Bournemouth failed in an attempt to sign Terry on loan during the January transfer window and are lining up a second assault as a result.
"I feel I still have regular football in me but understand that opportunities here at Chelsea will be limited, it is therefore time for a new challenge".
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The Swans will make a move for Chelsea stalwart John Terry if they remain in the Premier League, as the club finds itself in a relegation battle.
Someday, Terry intends to return to Chelsea to work amongst the coaching staff and maybe as the head coach to continue from where he stopped.
"Wearing the armband and being your captain has been without a doubt one of the proudest achievements of my life".
"I want to stress that the journey is not yet over".
However, the club are determined to find him a role sooner rather than later and he added: "I look forward to returning to this great club in some capacity in the future".
"Whether that will be with West Ham or elsewhere I don't know, we don't think about that right now but I don't think it is the end of John Terry's career. I will of course always be a Blue and am desperate to end my final season as a Chelsea player with more silverware".
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