Bradbury has confirmed the Cherries have made the 20-year-old right-back, who was on-loan at Dean Court from Tottenham last season, a 'good offer' in an attempt to seal his return to the club.
"We put an offer to Adam Smith - a good offer as well - to make him a Bournemouth player," Bradbury told the Daily Echo.
"I would like to think the time he had at the club - which he said he enjoyed and he enjoyed the way we played - means that it is definitely an option for him.
"He is a player we would certainly like to keep, hence the offer we put to him was decent."
Smith is available on a free transfer after his contract at Tottenham expired.
Source: Team Talk
Source: Team Talk