The Potters' £20m bid for 22-year-old Berahino was rejected but a £13m offer for Wales international Allen, 26, has been accepted.
"You can never second guess deals," Hughes told BBC Radio Stoke.
"Ideally you want to do all your business before the season starts."
Stoke are yet to go back with an improved offer for Berahino, with Albion thought to be keen to bring in a potential replacement first.
"Things are ongoing - we're very hopeful over a number of deals we're involved with but until they are actually done you can never be too sure," Hughes said.
"Sometimes the deals seem quite easy and others seem to drag on, which a number of them have this time unfortunately, but we just have to wait and be patient - sometimes other clubs need to do business first."
Stoke's preparations for the new season continue with a 10-day pre-season tour of Florida.
Manager Mark Hughes says Stoke City are happy to bide their time in their attempts to sign West Bromwich Albion striker Saido Berahino and Liverpool midfielder Joe Allen.