Jakupovic has made just 10 appearances for Hull since joining in 2012 and the one-time Switzerland international had a spell on loan at League One Leyton Orient last season.
The 29-year-old made his top-flight debut against Manchester United in May but found himself behind Allan McGregor and Steve Harper in the pecking order at the KC Stadium.
With Steve Bruce's team set to embark on a UEFA Europa League campaign - which begins with a third qualifying round tie against an as yet unknown opponent at the end of the month - Jakupovic may be called upon to ease the burden on Scotland international McGregor.
Hull, who qualified for Europe after reaching the FA Cup final last season, begin their league campaign with a visit to newly promoted QPR on August 16.
