Maley, 37, joined the Lions in 2016 when the club was in League One and is currently third-choice at the Tony Macaroni Arena - as well as being the only part-time player in the Premiership.
He has found first-team opportunities limited in West Lothian but has received praise from manager Gary Holt for his influence on the dressing room.
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However, with his current contract due to expire in June - and in what Livingston described as "quite possibly a football first" - Maley's fate has been put in the hands of social media users as the club posted a poll on Twitter.
The club's tweet read: "With his contract expiring next month, we’re leaving it in the hands of the fans as to whether or not we offer "Stretch” an extension.
"Stay or go - you decide!"
Speaking in December, Holt praised the impact Maley had in his role at Livingston: "I have to give the big man some plaudits. He does get a lot of stick but there’s nothing happier sometimes than when you see people sitting in the stand smiling who have played their part."
The club's Twitter poll attracted comments from Maley's colleagues at the Tony Macaroni Arena, with midfielder Marvin Bartley and assistant manager David Martindale among those to reply to the post.
"One hundred per cent he goes, can’t push forward as a club with ‘players’ like him!" Bartley joked. "Bye big man, look after yourself."
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