Birmingham and Blackburn have both been scouting the 23-year-old throughout the campaign, and they have been impressed by his form.
Bradshaw has scored 18 goals to date this season, and his impressive record has been a major reason behind the Midlands club’s push for promotion from League One.
Walsall are reportedly determined to keep hold of their star front man, and they have already rejected offers from Huddersfield Town and Bristol City.
However, Bradshaw has just over a year remaining on his contract, meaning that their bargaining position is weakening.
Birmingham and Blackburn are now weighing up the possibility of making a bid in the summer, as they look to improve their attacking options.
The pair have both struggled to score with frequency this season, and there are hopes that Bradshaw could make the step up to the second tier, if he was to sign.