Manager Joe Royle has handed the duo free transfers as he feels the club's academy is ready to produce more talent, which means he need to free up space in his squad.
"The likes of Antonio Murray, Gerard Nash and Scott Mitchell have been pushing through ahead of the two lads so we felt it was in their best interests if we allowed them to find first-team football elsewhere," Royle told the club's website.
"They are both smashing lads and hopefully clubs will come in and give them a chance to get their careers going in league football, which is what they need now.
"They are still under contract here though and will of course remain part of the set-up unless a move becomes apparent."
Both players are England youth internationals and are expected to find clubs quickly.
Bloomfield was the subject of a bid from Newcastle United earlier this year, but has failed to fulfil his potential - likewise with Hogg (pictured) who arrived with a big reputation from York in June 2001.
