The midfielder has spent the past four weeks at Belle Vue and manager Sean O'Driscoll, who worked with Stock at his previous club Bournemouth, is hopeing to extend the deal.
He said: "I have spoken to Brian and he is glad to be playing first-team football again and he is happy to stay on at the club.
"I'll be having a word with Preston this week and hopefully there won't be a problem - especially as they will be able to recall him at 24-hours' notice."