The 23-year-old was offered a fresh deal by manager Eddie Howe after his previous contract ran out Wednesday.
Allsop joined the Cherries from Leyton Orient in January 2013 and was a key member in the promotion from League One in 2012, and featured in the Championship the following season.
He then missed a large part of the season due to a bout of glandular fever and ended up going out on loan to Coventry City at the start of the 2014/15 season.
Allsop made 27 appearances for the Sky Blues during his loan.
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